LIBRARY  OF  THE 
UNIVERSITY  OF  ILLINOIS 
AT  URBANA-CHAMPAIGN 


193 

L53d 
1908 


27 
APR  10 


JAN 
DtC  0  9 

.MAY 


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JUL14 


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L161  — Q-1096 


THE  LEIBNIZ  MONUMENT  NEAR  THE  THOMAS-KIRCHE  IN  LEIPSIC. 


LEIBNIZ 


DISCOURSE  ON  METAPHYSICS 

CORRESPONDENCE  WITH  ARNAULD 

AND   MONADOLOGY 


WITH  AN  INTRODUCTION  BY  PAUL  JANET, 
MEMBER     OF     THE     FRENCH      INSTITUTE. 


TRANSLATED  BY 

DR.  GEORGE  R.   MONTGOMERY 

INSTRUCTOR  IN  PHILOSOPHY  IN  VALE  UNIVERSITY 


CHICAGO 
THE  OPEN  COURT  PUBLISHING  COMPANY 

LONDON  AGENTS 

KKGAN  PAUL,  TRENCH,  TRUBNER  &  Co.,  LTD. 
1908 


TRANSLATION  COPYRIGHTED 

BY 

THE  OPEN  COURT  PUBLISHING  Co. 
1902. 


/•fog 


EDITOR'S   PREFACE. 


The  present  volume  of  Leibniz's  writings,  which  now  takes 
its  place  in  the  "Philosophical  Classics"  alongside  the  works  of 
Descartes,  Berkeley,  Hume,  and  Immanuel  Kant,  is  made  up 
of  three  separate  treatises:  (i)  The  Discourse  on  Meta- 
physics, (2)  Leibniz's  Correspondence  with  Arnauld,  and 
(2)  The  Monadology.  Together  they  form  a  composite  and 
logical  whole,  and  afford  an  excellent  survey  of  Leibniz's 
thought.  The  first  two,  the  Metaphysics  and  the  Corre- 
spondence with  Arnauld,  have  never  before  been  translated 
into  English,  while  the  translation  of  the  Monadology  is  new. 
The  thanks  of  the  public  for  this  translation  are  due  to  Dr. 
George  R.  Montgomery,  instructor  in  philosophy  in  Yale 
University,  and  for  the  suggestion  of  making  the  translation 
to  Dr.  G.  M.  Duncan,  professor  of  philosophy  in  Yale  Univer- 
sity. The  clear  and  admirable  resume  of  the  history  of 
philosophy  in  Libniz's  time  and  of  his  own  system  from  the 
pen  of  the  late  Paul  Janet,  Member  of  the  French  Institute, 
was  added  at  the  suggestion  of  the  editor.  Thus  with  the 
index,  all  the  necessary  material  has  been  furnished  in  this 
volume  for  a  comprehension  of  the  thought  of  one  of  the  most 
versatile  geniuses  the  world  has  produced. 

"What  a  marvellously  gifted  man  Leibniz  was!"  admirably 
remarks  Dr.  Duncan.  '  'The  king  of  Prussia  truly  said  of  him, 
'He  represents  in  himself  a  whole  Academy' ;  and  George  I.  of 
England  was  quite  justified  in  saying,  'I  count  myself  happy 
in  possessing  two  kingdoms,  in  one  of  which  I  have  the  honor 
of  reckoning  a  Leibniz,  and  in  the  other  a  Newton,  among  my 
subjects. '  A  brilliant  mathematician,  contesting  with  Newton 
the  honor  of  discovering  the  Calculus;  a  gifted  psychologist 
and  epistemologist,  equalling  and  surpassing,  in  his  New 
Essays,  Locke's  famous  Essay;  a  profound  theologian,  writing 
the  most  famous  book  on  Theodicy  which  has  ever  been  printed ; 
a  learned  historian,  producing  a  history  of  the  House  of 
Brunswick  commended  by  Gibbon  himself;  a  far-sighted 
statesman  and  diplomatist,  honored  at  several  of  the  most 
powerful  courts  of  Europe;  a  great  philosopher,  founder  of 


IV  EDITOR  S    PREFACE. 

modern  German  speculative  philosophy  and  worthy  to  be 
named  with  Kant  himself;  and,  withal,  an  eminent  scientist, 
'a  man  of  science,  in  the  modern  sense,  of  the  first  rank,'  as 
Professor  Huxley  calls  him, — these  are  a  few  of  his  claims  to 
consideration. ' ' 

And  the  same  author  remarks  as  to  the  value  of  the  present 
selection  from  his  writings: 

"The  profound  and  quickening  thought  of  this  most  com- 
prehensive thinker  since  Aristotle  was  never  presented  by  him 
in  a  more  simple  and  untechnical  form  than  in  his  Discourse 
on  Metaphysics  and  the  correspondence  with  Arnauld  relating 
thereto.  These  together  with  the  Monadology,  the  last  sys- 
tematic presentation  of  his  philosophy  written  by  him  a  quarter 
of  a  century  later,  are  here,  at  a  nominal  price,  made  accessible 
to  the  general  reading  public  and  to  university  students.  If 
one  will  read  these  letters  between  Leibniz  and  Arnauld,  and 
then  the  Discourse  on  Metaphysics,  and  finally  the  Monad- 
ology— and  that  is  the  best  order  in  which  to  read  the  book — 
one  will  be  introduced  in  the  simplest  and  the  best  possible 
way  to  Leibniz's  philosophy.  The  Discourse  on  Metaphysics 
is  probably  the  best  account  of  his  philosophy  which  he  ever 
wrote.  His  views  underwent  but  little  modification  between 
the  writing  of  the  Discourse  of  Metaphysics  and  the  writing 
of  the  Monadology.  The  only  important  difference  is  in  the 
introduction  in  the  latter  of  a  more  artificial  terminology." 

In  the  present  volume,  therefore,  The  Open  Court  Pub- 
lishing Company  hopes  to  have  rendered  a  considerable  service 
to  the  philosophical  public. 

THOMAS  J.  McCORMACK. 

LA  SALLE,  ILL., 
August  20,  1902. 


CONTENTS. 

PAGE 

THE  LEIBNIZ  MONUMENT  NEAR    THE  THOMAS-KIRCHE  IN 

LEIPZIG ;  Frontispiece 

INTRODUCTION  BY  PAUL  JANET VII 

DISCOURSE  ON  METAPHYSICS i 

CORRESPONDENCE  BETWEEN  LEIBNIZ  AND  ARNAULD  .        .      65 
MONADOLOGY 249 


INTRODUCTION. 

By  PAUL  JANET. 

When  Descartes,  in  the  first  half  of  the  seventeenth  century, 
said  that  there  are  only  two  kinds  of  things  or  substances 
in  nature,  namely,  extended  substances  and  thinking  substances, 
or  bodies  and  spirits ;  that,  in  bodies,  everything  is  reducible  to 
extension  with  its  modifications  of  form,  divisibility,  rest  and 
motion,  while  in  the  soul  everything  is  reducible  to  thinking 
with  its  various  modes  of  pleasure,  pain,  affirmation,  reason- 
ing, will,  etc.  .  .  ;  when  he  in  fact  reduced  all  nature  to  a 
vast  mechanism,  outside  of  which  there  is  nothing  but  the 
soul  which  manifests  to  itself  its  existence  and  its  independ- 
ence through  the  consciousness  of  its  thinking,  he  brought 
about  the  most  important  revolution  in  modern  philosophy.  To 
understand  its  significance  however  an  account  must  be  given 
of  the  philosophical  standpoint  of  the  time. 

In  all  the  schools  at  that  time  the  dominant  theory  was  that 
of  the  Peripatetics,  altered  by  time  and  misunderstood,  the 
theory  of  substantial  forms.  It  posited  in  each  kind  of  sub- 
stance a  special  entity  which  constituted  the  reality  and  the 
specific  difference  of  that  substance  independently  of  the  rela- 
tion of  its  parts.  For  example,  according  to  a  Peripatetic  of  the 
time,  "fire  differs  from  water  not  only  through  the  position  of 
its  parts  but  through  an  entity  which  belongs  to  it  quite  dis- 
tinct from  the  materials.  When  a  body  changes  its  condition, 
there  is  no  change  in  the  parts,  but  one  form  is  supplanted  by 
another."*  Thus,  when  water  becomes  ice,  the  Peripatetics 
claimed  that  a  new  form  substituted  itself  in  place  of  the  pre- 
ceding form  to  constitute  a  new  body.  Not  only  did  they 
admit  primary  or  basal  entities,  or  substantial  forms  to  explain 
the  differences  in  substances,  but  for  small  changes  also,  and 
for  all  the  sensible  qualities  they  had  what  were  called  acci- 
dental forms:  thus  hardness,  heat,  light  were  beings  quite 
different  from  the  bodies  in  which  they  were  found. 

*L-  P.  I/agrange,  Les  Principes  de  la  Philosophie  contre  les  Nouveaux 
Philosophes. — See  Bouillier's  Histoire  de  la  Philosophie  Cariesienne,  Vol. 
I.  Chap.  26. 

VII 


VIII  INTRODUCTION. 

To  avoid  the  difficulties  inherent  in  this  theory,  the  School- 
men were  led  to  adopt  infinite  divisions  among  the  substantial 
forms.  In  this  way  the  Jesuits  of  Coimbre  admitted  three  kinds 
of  these  forms:  first,  the  being  which  does  not  receive  its  exist- 
ence from  a  superior  being  and  is  not  received  into  an  inferior 
subject, — this  being  is  God ;  second,  the  forces  which  receive 
their  being  from  elsewhere  without  being  themselves  received 
into  matter, — these  are  the  forms  which  are  entirely  free  from 
any  corporeal  concretion ;  third,  the  forms  dependent  in  every 
respect,  which  obtain  their  being  from  a  superior  cause  and 
are  received  into  a  subject, — these  are  the  accidents  and  the 
substantial  forms  which  determine  matter. 

Other  Schoolmen  adopted  divisions  still  more  minute  and 
distinguished  six  classes  of  substantial  forms,  as  follows:  first, 
the  forms  of  primary  matter  or  of  the  elements ;  second,  those 
of  inferior  compounds,  like  stones ;  third,  those  of  higher  com- 
pounds, like  drugs ;  fourth  those  of  living  beings,  like  plants ; 
fifth,  those  of  sensible  beings,  like  animals;  sixth,  above  all 
the  rest,  the  reasoning  (rationalis)  substantial  form  which  is 
like  the  others  in  so  far  as  it  is  the  form  of  a  body  but  which 
does  not  derive  from  the  body  its  special  function  of  thinking. 

Some  have  thought,  perhaps,  that  Moliere,  Nicole,  Male- 
branche  and  all  those  who  in  the  seventeenth  century  ridiculed 
the  substantial  forms,  calumniated  the  Peripatetic  Schoolmen 
and  gratuitously  imputed  absurdities  to  them.  But  they 
should  read  the  following  explanation,  given  by  Toletus,  of 
the  production  of  fire:  "The  substantial  form  of  fire,"  says 
Toletus,  "is  an  active  principle  by  which  fire  with  heat  for  an 
instrument  produces  fire."  Is  not  this  explanation  even  more 
absurd  than  the  -virtus  dormitivaf  The  author  goes  on  to 
raise  an  objection,  that  fire  does  not  always  come  from  fire. 
To  explain  this  he  proceeds,  "I  reply  that  there  is  the  great- 
est difference  between  the  accidental  and  the  substantial  forms. 
The  accidental  forms  have  not  only  a  repugnance  but  a 
definite  repugnance,  as  between  white  and  black,  while 
between  substantial  forms  there  is  a  certain  repugnance  but  it 
is  not  definite,  because  the  substantial  form  repels  equally  all 
things.  Therefore  it  follows  that  white  which  is  an  accidental 
form  results  only  from  white  and  not  from  black,  while  fire 
can  result  from  all  the  substantial  forms  capable  of  producing  it 
in  air,  in  water  or  in  any  other  thing." 


INTRODUCTION.  IX 

The  theory  of  substantial  or  accidental  forms  did  more  than 
to  lead  to  nonsense  like  the  above ;  it  introduced  errors  which 
stood  in  the  way  of  any  clear  investigation  of  real  causes.  For 
example,  since  some  bodies  fell  toward  the  earth  while  others 
rose  in  the  air,  it  was  said  that  gravity  was  the  substantial  form 
of  the  former  and  lightness  of  the  latter.  Thus  heavy  and 
light  bodies  were  distinguished  as  two  classes  of  bodies  having 
properties  essentially  different,  and  they  were  kept  from  the 
inquiry  whether  these  apparently  different  phenomena  did  not 
have  an  identical  cause  and  could  not  be  explained  by  the  same 
law.  It  was  thus  again  that  seeing  water  rise  in  an  empty 
tube,  instead  of  inquiring  under  what  more  general  fact  this 
phenomena  could  be  subserved,  they  imagined  a  -virtue,  an 
occult  quality,  a  hatred  on  the  part  of  the  vacuum,  and  this 
not  only  concealed  the  ignorance  under  a  word  void  of  sense 
but  it  made  science  impossible  because  a  metaphor  was  taken 
for  an  explanation. 

So  great  had  become  the  abuse  of  the  substantial  forms,  the 
occult  qualities,  the  sympathetic  virtues,  etc.,  that  it  was  a 
true  deliverance  when  Gassendi  on  the  one  hand  and  Descartes 
on  the  other  founded  a  new  physics  on  the  principle  that  there 
is  nothing  in  the  body  which  is  not  contained  in  the  mere 
conception  of  bodies,  namely  extension.  According  to  these 
new  philosopners  all  the  phenomena  of  bodies  are  only  modi- 
fications of  extension  and  should  be  explained  by  the  proper- 
ties inherent  in  extension,  namely,  form,  position,  and  motion. 
Upon  this  principle  nothing  happens  in  bodies  of  which  the 
understanding  is  not  able  to  form  a  clear  and  distinct  idea. 
Modern  physics  seems  to  have  partially  confirmed  this  theory, 
when  it  explains  sound  and  light  by  movements  (vibrations, 
undulations,  oscillations,  etc.),  either  of  air  or  of  ether 

It  has  often  been  said  that  the  march  of  modern  science  has 
been  in  the  opposite  direction  from  the  Cartesian  philosophy, 
in  that  the  latter  conceives  of  matter  as  a  dead  and  inert  sub- 
stance while  the  former  represents  it  as  animated  by  forces, 
activities  and  energies  of  every  kind.  This  it  seems  to  me  is 
to  confuse  two  wholly  different  points  of  view,  that  is  the  phys- 
ical and  the  metaphysical  points  of  view.  The  fact  seems  to 
be  that  from  the  physical  point  of  view,  science  has  rather 
followed  the  line  of  Descartes,  reducing  the  number  of  occult 
qualities  and  as  far  as  possible  explaining  all  the  phenomena 


X  INTRODUCTION. 

in  terms  of  motion.  In  this  way  all  the  problems  tend  to 
become  problems  of  mechanics ;  change  of  position,  change  of 
form,  change  of  motion — these  are  the  principles  to  which  our 
physicists  and  our  chemists  have  recourse  whenever  they  can. 
It  is  therefore  wrong  to  say  that  the  Cartesian  line  of 
thought  has  completely  failed  and  that  modern  science  has 
been  moving  away  from  it  more  and  more.  On  the  contrary 
we  are  witnessing  the  daily  extension  of  mechanicalism  in  the 
science  of  our  time.  The  question  takes  on  a  different  phase 
when  it  is  asked  whether  mechanicalism  is  the  final  word  of 
nature,  whether  it  is  self-sufficient,  in  fact  whether  the  princi- 
ples of  mechanicalism  are  themselves  mechanical.  This  is  a 
wholly  metaphysical  question  and  does  not  at  all  affect  positive 
science ;  for  the  phenomena  will  be  explained  in  the  same  way 
whether  matter  is  thought  of  as  inert,  composed  of  little  par- 
ticles which  are  moved  and  combined  by  invisible  hands,  or 
whether  an  interior  activity  and  a  sort  of  spontaneity  is 
attributed  to  them.  For  the  physicist  and  for  the  chemist, 
forces  are  only  words  representing  unknown  causes.  For  the 
metaphysician  they  are  real  activities.  It  is  metaphysics, 
therefore,  and  not  physics  which  is  rising  above  mechanicalism. 
It  is  in  metaphysics  that  mechanicalism  has  found,  not  its 
contradiction,  but  its  completion  through  the  doctrine  of  dyn- 
amism. It  is  this  latter  direction  that  philosophy  has  mainly 
taken  since  Descartes  and  in  this  the  prime  mover  was 
Leibniz.* 


*  We  give  here  in  a  note  the  resume  of  Leibniz's  life  and  the  names  of 
his  principal  works.  Leibniz  (Gottfried  Wilhelm)  was  born  at  Leipzig  in 
1646.  He  lost  his  father  at  the  age  of  six  years.  From  his  very  infancy  he 
gave  evidence  of  remarkable  ability.  At  fifteen  years  of  age  he  was  ad- 
mitted to  the  higher  branches  of  study  (philosophy  and  mathematics)  which 
he  pursued  first  at  Leipzig  and  then  at  Jena.  An  intrigue  not  very  well 
understood  prevented  his  obtaining  his  doctor's  degree  at  Leipzig  and  he 
obtained  it  from  the  small  university  of  Altdorf  near  Nuremberg,  where  he 
made  the  acquaintance  of  Baron  von  Boineburg,  who  became  one  of  his 
most  intimate  friends  and  who  took  him  to  Frankfort.  Here  he  was  named 
as  a  councillor  of  the  supreme  court  in  the  electorate  of  Mainz,  and  wrote 
his  first  two  works  on  j  urisprudence.  The  Study  of  Law  and  The  Reform  of 
the  Corpus  Juris.  At  Frankfort  also  were  written  his  first  literary  and 
philosophical  works  and  notably  his  two  treatises  on  motion:  Abstract  Mo- 
tion, addressed  to  the  Academy  of  Sciences  at  Paris,  and  Concrete  Motion, 
addressed  to  the  Royal  Society  at  London.  He  remained  with  the  Elector 
till  the  year  1672,  when  he  began  his  journeys.  He  first  went  to  Paris  and 
then  to  London,  where  he  was  made  a  member  of  the  Royal  Society.  Re- 
turning to  Paris  he  remained  till  1677,  when  he  made  a  trip  through  Hol- 
land, and  finally  took  up  his  residence  at  Hanover,  where  he  was  appointed 
director  of  the  library.  At  Hanover  he  lived  for  ten  years,  leading  a  very 


INTRODUCTION.  XI 

In  order  to  understand  Leibniz's  system  we  must  not  forget  a 
point  to  which  sufficient  attention  has  not  been  paid,  namely, 
that  Leibniz  never  gave  up  or  rejected  the  mechanicalism  of 
Decartes.  He  always  affirmed  that  everything  in  nature 
could  be  explained  mechanically ;  that,  in  the  explanation  of 
phenomena,  recourse  must  never  be  had  to  occult  causes ;  so 
far  indeed  did  he  press  this  position  that  he  refused  to  admit 
Newton's  attraction  of  gravitation,  suspecting  it  of  being  an 
occult  quality :  while,  however,  Leibniz  admitted  with  Descartes 
the  application  of  mechanicalism  he  differed  from  him  in  regard 
to  the  basis  of  it  and  he  is  continually  repeating  that  if  every- 
thing in  nature  is  mechanical,  geometrical  and  mathematical 
the  source  of  mechanicalism  is  in  metaphysics.* 

Descartes  explained  everything  geometrically  and  mechani- 


busy  life.  He  contributed  to  the  founding  of  the  Ada  Eruditorum,  a  sort  of 
journalof  learning.  From  168710  1691,31  the  request  ofhis  patron,  Duke 
Ernst-Augustus,  he  was  engaged  in  searching  various  archives  in  Ger- 
many and  Italy  for  the  writing  of  the  history  of  the  house  of  Brunswick.  To 
him  the  Academy  of  Berlin,  of  which  he  was  the  first  president,  owes  its 
foundation.  The  last  fifteen  years  of  his  life  were  given  up  principally  to 
philosophy.  In  this  period  must  be  placed  the  New  Essays,  the  "Theodicy, 
the  Monadology,  and  also  his  correspondence  with  Clarke,  which  was 
interrupted  by  his  death— November  14,  1716.  For  fuller  details,  see 
Guhrauer's  learned  and  complete  biography,  2  yols,  Breslau,  1846.  During 
the  life-time  of  Leibniz,  aside  from  the  articles  in  journals,  only  some  five 
of  his  writings  were  published,  including  his  doctor's  thesis,  De  Principle 
Individui  (1663),  and  the  Theodicee  (1710).  After  his  death  (1716)  all  his  papers 
were  deposited  in  the  library  at  Hanover,  where  they  are  to-day,  a  great 
part  of  them  (15,000  letters)  still  unpublished.  In  1717-1719  appeared  the 
Correspondence  with  Locke;  in  1720  a  German  translation  of  the  Mon- 
adology; in  1765  his  Oeuvres  Philosophiques,  etc.,  includingthe  New  Essays  on 
the  Human  understanding;  in  1768  Duten's  edition  of  his  works  in  six  vol- 
umes; in  1840  appeared  Erdmann's  edition  of  his  works,  including  among 
other  unpublished  writings  the  original  French  of  the  Monadology.  The 
Correspondence  with  Arnauld  and  the  Treatise  on  Metaphysics  were  first 
published  by  Grotefend  in  1840.  Gerhardt  published  Leibniz's  math- 
ematical works  1843  to  1863,  and  the  Philosophical  Works  (seven  volumes), 
1875-1890.  In  1900  Paul  Janet,  who  had  already  published  the  Philosophical 
Works  (1866)  in  two  volumes,  brought  out  a  second  edition,  revised  and  en- 
larged. The  first  English  translation  of  Leibniz's  works  was  made  by 
Professor  G.  M.  Duncan,  who  included  in  one  volume  all  of  the  better 
known  shorter  works  (1890).  This  was  followed  in  1896  with  a  translation 
of  the  New  Essays  by  A.  G.  Langley.  Latta's  translation  of  some  of  the 
shorter  works,  including  the  Monadology,  has  earned  a  well-merited  reputa- 
tion, and  Russell's  work  on  Leibniz's  philosophy  contains  much  that  is 
suggestive  to  a  translator. 

'Letter  to  Schulemburg  (Dutens,  T.  Ill,  p.  332):  "The  Cartesians  rightly 
felt  that  all  particular  phenomena  of  bodies  are  produced  mechanically,  but 
they  failed  to  see  that  the  sources  of  mechanicalism  in  turn  arise  in  some 
other  cause."  Letter  to  Reniond  de  Montmort  (Erdman,  Opera  Philo- 
sophica,^.  702):  "When  I  seek  for  the  ultimate  reasons  of  mechanicalism 
and  the  laws  of  motion  I  am  surprised  to  discover  that  they  are  not  to  be 
found  in  mathematics  and  that  we  must  turn  to  metaphysics." — See  also: 
De  Natura  Ipsa,  3;  De  Origine  Radicali;  Animadversiones  in  Cartesiunt 
Guhrauer,  p.  80),  etc. 


XII  INTRODUCTION. 

cally,  that  is  by  extension,  form,  and  motion,  just  as  Democritus 
had  done  before ;  but  he  did  not  go  farther,  finding  in  exten- 
sion the  very  essence  of  corporeal  substance.  Leibniz's  genius 
showed  itself  when  he  pointed  out  that  extension  does  not 
suffice  to  explain  phenomena  and  that  it  has  need  itself  of  an 
explanation.  Brought  up  in  the  scholastic  and  peripatetic 
philosophy,  he  was  naturally  predisposed  to  accord  more  of 
reality  to  the  corporeal  substance,  and  his  own  reflections  soon 
carried  him  much  farther  along  the  same  line. 

It  is  also  worth  noticing,  as  Guhrauer  has  said  in  his  Life  of 
Leibniz,  that  it  was  a  theological  problem  which  put  Leibniz 
upon  the  track  of  reforming  the  conception  of  substance.  The 
question  was  rife  as  to  the  real  presence  in  transubstantia- 
tion.  This  problem  seemed  inexplicable  upon  the  Cartesian 
hypothesis,  for  if  the  essence  of  a  body  is  its  extension,  it  is  a 
contradiction  that  the  same  body  can  be  found  in  several  places 
at  the  same  time.  Leibniz,  writing  to  Arnauld  in  1671,  says 
he  thinks  he  has  found  the  solution  to  this  great  problem,  since 
he  has  discovered  '  'that  the  essence  of  a  body  does  not  consist 
in  extension,  that  the  corporeal  substance,  even  taken  by 
itself,  is  not  extension  and  is  not  subject  to  the  conditions  of 
extension.  This  would  have  been  evident  if  the  real  character 
of  substance  had  been  discovered  sooner." 

Leaving  aside  this  point,  however,  the  following  are  the 
different  considerations  which  led  Leibniz  to  admit  non- 
mechanical  principles  as  above  corporeal  mechanicalism,  and  to 
reduce  the  idea  of  the  body  to  the  idea  of  active  indivisible  sub- 
stances, entelechies  or  monads,  having  innate  within  them- 
selves the  reason  for  all  their  determinations. 

i.  The  first  and  principal  reason  which  Leibniz  brings  up 
against  Descartes  is  that,  "If  all  that  there  is  in  bodies  is 
extension  and  the  position  of  the  parts,  then  when  two  bodies 
come  into  contact  and  move  on  together  after  the  contact, 
that  one  which  was  in  motion  will  carry  along  the  body  at  rest 
without  losing  any  of  its  velocity,  and  the  difference  in  the  sizes 
of  the  bodies  will  effect  no  change,"  which  is  contrary  to  expe- 
rience. A  body  in  motion  which  comes  in  contact  with  one  at 
rest  loses  some  of  its  velocity  and  its  direction  is  modified, 
which  would  not  happen  if  the  body  were  purely  passive. 
"Higher  conceptions  must  therefore  be  added  to  extension, 
namely,  the  conceptions  of  substance,  action  and  force ;  these 


INTRODUCTION.  XIII 

latter  carry  the  idea  that  that  which  suffers  action,  acts  recipro- 
cally and  that  that  which  acts  is  reacted  upon."  * 

2.  Extension  cannot    serve    to    give  the    reason    for    the 
changes  which  take  place  in  bodies,  for  extension  with  its 
various  modifications  constitutes  what  is  called  in  the  school 
terminology  extrinsic  characteristics,  whence  nothing  can  result 
for  the  being  itself ;  whether  a  body  be  round  or  square  does 
not  affect  its  interior  condition,  nor  can  any  particular  change 
result  for  it.  f     Furthermore  every  philosophy  which  is  exclu- 
sively mechanical  is  obliged  to  deny  change  and  to  hold  that 
everything  is  changeless  and  that  there  are  only  modifications 
of  position  or  displacements  in  space  or  motion.     Who  does 
not  see,  however,  that  motion  itself  is  a  change,  and  should 
have  its  reason  in  the  being  which  moves  or  which  is  moved, 
for  even  passive  motion  must  correspond  to  something  in  the 
essence  of  the  body  moved?    Besides    if   corporeal  elements 
differ  from  one  another  through  form,  why  have  they  one  form 
rather  than  any  other?     Epicurus  talks  to  us  of  round  and 
hooked  atoms.      Why  is  a  certain  atom  round  and  another 
hooked?    Should  not  the  reason  be  in  the  very  substance  of  the 
atom?    Therefore  form,  position,  motion  and  all  the  extrinsic 
modifications  of  bodies    should    emanate    from  an    internal 
principle  analogous  to  that  which  Aristotle  calls  nature  or 
entelechy.  \ 

3.  Extension  cannot  be  substance.     On  the  contrary  it  pre- 
supposes substance.     "Aside  from  extension  there  must  be  a 
subject  which  is  extended,  that  is,  a  substance  to  which  con- 
tinuity appertains.     For  extension  signifies  only  a  continued 
repetition  or  multiplication  of  that  which  is  expanded,  a  plu- 
rality, a  continuity  or  co-existence  of  parts  and  consequently  it 
does  not  suffice  to  explain  the  real  nature  of  expanded  or  repeated 
substance  whose  conception  precedes  that  of  repetition."  § 

4.  Another  reason  given  by  Leibniz  is  that  the  conception  of 

*  Letter,  Whether  the  essence  of  bodies  consists  in  extension,  1691  (Erd- 
maim,  Vol.  27,  p.  112). 


&uur>iiiui_c  aiiuuiu.    —  ivClici   LU  .ni  uduiu* 

\Confessio  Naturae  Contra  Artheista,  1668,  Erdm.,  p.  45.  Leibniz  in 
this  little  treatise  proves:  ist,  that  bodies  and  indeed  atoms  have  not  in 
themselves  the  reason  for  their  forms;  2d,  that  they  have  not  the  reason  for 
their  motion:  3d,  that  they  have  not  the  reason  for  their  coherence. 

§  Extract  from  a  letter  (Erdmann,  Vol.  28,  p.  115):  Examination  of  the 
principles  of  Malebranche  (Erdmanu,  p.  692). 


XIV  INTRODUCTION. 

substance  necessarily  implies  the  idea  of  unity.  No  one  thinks 
that  two  stones  very  far  apart  form  a  single  substance.  If  now 
we  imagine  them  joined  and  soldered  together,  will  this  juxta- 
position change  the  nature  of  things?  Of  course  not;  there 
will  always  be  two  stones  and  not  a  single  one.  If  now  we 
imagine  them  attached  by  an  irresistible  force,  the 'impossibility 
of  separating  them  will  not  prevent  the  mind  from  distin- 
guishing them  and  will  not  prevent  their  remaining  two  and 
not  one.  In  a  word  every  compound  is  no  more  a  single  sub- 
stance than  is  a  pile  of  sand  or  a  sack  of  wheat.  We  might 
as  well  say  that  the  employees  of  the  India  Company  formed 
a  single  substance.*  It  is  evident  therefore  that  a  compound 
is  never  a  substance  and  in  order  to  find  the  real  substance  we 
must  attain  unity  or  the  indivisible.  To  say  that  there  are  no 
such  unities  is  to  say  that  matter  has  no  elements,  in  other 
words  that  it  is  not  made  up  of  substance  but  it  is  a  pure  phe- 
nomenon like  the  rainbow.  The  conclusion  is  then  either  that 
matter  has  no  substantial  reality  or  else  it  must  be  admitted 
that  it  is  reducible  to  simple  and  consequently  unextended 
elements,  called  monads, 

5.  Leibniz  brings  forward  another  argument  in  behalf  of 
his  theory  of  monads.  This  is  that  the  essence  of  every  sub- 
stance is  in  force,  which  fact  is  as  true  of  the  soul  as  of  the  body. 
It  can  be  proved  a  priori.  Is  it  not  evident  that  a  being  really 
exists  only  in  so  far  as  it  acts?  A  being  absolutely  passive 
would  be  a  pure  nothing,  and  would  involve  a  contradiction ; 
or,  by  hypothesis,  receiving  everything  from  outside  and  hav- 
ing nothing  through  itself,  it  would  have  no  characteristic,  no 
attribute  and  hence  would  be  a  pure  nothing.  The  mere  fact 
of  existence,  therefore,  already  supposes  a  certain  force  and  a 
certain  energy. 

Leibniz  presses  this  thought  of  the  activity  of  substances  so 
far  that  he  even  admits  no  degree  of  passivity.  According  to 

*  "  If  the  parts  which  act  together  for  a  common  purpose,  more  properly 
compose  a  substance  than  do  those  which  are  in  contact,  then  all  the  offi- 
cials of  the  India  Company  would  much  better  constitute  a  real  substance 
than  would  a  pile  of  stones.  What  else,  however,  is  a  common  purpose 
rather  than  a  resemblance  or  indeed  an  orderliness  which  our  minds  notice 
in  different  things?  If  on  the  other  hand  the  unity  by  contact  be  made  the 
basis,  other  difficulties  arise.  The  parts  of  solid  bodies  are  united  perhaps 
only  by  the  pressure  of  surrounding  bodies,  while  inthemselves  and  ifc  their 
substance  there  is  no  more  union  than  in  a  heap  of  sand,  arena  sine  calce. 
Why  do  many  rings  when  interlaced  to  form  a  chain  compose  a  veritable 
substance  rather  than  when  there  are  openings  so  that  they  can  be  taken 
apart?  .  .  .  They  are  all  fictions  of  the  mind."  (Letter  to  Arnauld;. 


INTRODUCTION  XV 

him,  no  substance  is,  properly  speaking,  passive.  Passion  in 
a  substance  is  nothing  else  than  an  action  considered  bound 
to  another  action  in  another  substance.  Every  substance  acts 
only  through  itself  and  cannot  act  upon  any  other.  The 
monads  have  no  windows  through  which  to  receive  anything 
from  outside.  They  do  not  undergo  any  action  and  conse- 
quently are  never  passive.  All  that  takes  place  in  them  is  the 
spontaneous  development  of  their  own  essence.  All  that  there 
is,  is  that  the  states  of  each  one  correspond  to  the  states  of  all 
the  others.  When  we  consider  one  of  these  states  in  one 
monad  as  corresponding  to  a  certain  other  state  in  another 
monad,  in  such  a  way  that  the  latter  is  the  condition  of  the 
former,  the  first  state*  is  called  a  passion  and  the  second  an 
action.  There  is,  therefore,  between  all  monad-substances  a 
pre-established  harmony,  in  accordance  with  which  each  one 
represents  (or  expresses,  as  Leibniz  says)  the  whole  universe. 
But  this  is  ever  only  the  development  of  its  own  activity. 

In  restoring  to  created  substances  the  activity  which  the 
Cartesian  school  had  too  much  sacrificed,  Leibniz  thought  to 
contribute  to  the  clearer  distinction  between  the  created  and 
the  Creator.  He  justly  remarked  that  the  more  the  activity  of 
the  created  things  is  diminished,  the  more  necessary  becomes 
the  intervention  of  God,  in  such  a  way  that  if  all  activity  in 
created  things  is  suppressed,  then  we  must  say  that  it  is  God 
who  brings  everything  in  them  to  pass  and  who  is  at  the  same 
time  their  being  and  their  action  (operari  et  esse).  What 
difference,  however,  is  there  between  this  point  of  view  and 
that  of  Spinoza?  Would  we  not  thus  make  nature  the  life  and 
the  development  of  the  divine  nature?  In  fact,  by  this  hypothe- 
sis, nature  is  reduced  to  a  mass  of  modes  of  which  God  is  the 
substance.  He,  therefore,  is  all  that  there  is  of  reality  in  bodies 
as  well  as  in  spirits. 

To  these  -five  fundamental  reasons  given  by  Leibniz  it  will 
perhaps  be  allowed  us  to  add  a  few  particular  considerations. 

Those  who  deny  that  the  essence  of  bodies  is  only  in 
force,  either  admit  the  vacuum  with  the  atomists,  ancient  and 
modern,  or  else  like  the  Cartesians  they  do  not  admit  it.  Let 
us  take  up  each  of  these  positions  separately. 

For  the  atomists,  disciples  of  Democritus  and  of  Epicurus, 
or  of  Gassendi,  the  universe  is  composed  of  two  elements,  the 
vacuum  and  the  plenum,  on  the  one  hand  space  and  on  the 


XVI  INTRODUCTION. 

other  hand  bodies.  The  bodies  are  reducible  to  a  certain 
number  of  solid  corpuscles,  indivisible,  with  differing  forms, 
heavy  and  animated  by  an  essential  and  spontaneous  motion. 
These  are  the  atoms  which  by  their  coming  together  constitute 
bodies. 

Now  it  is  evident  that  atoms  in  taking  the  place  of  other 
atoms,  successively  occupy  in  empty  space  places  that  are 
adequate  to  them,  which  have  exactly  the  same  extension  and 
the  same  forms  as  the  respective  atoms.  If  at  the  moment 
when  an  atom  is  motionless  in  some  place  we  imagine  lines 
drawn  following  its  contours  (as  when  an  object  is  being  traced 
for  transferring),  is  it  not  clear  that  if  the  atom  were  removed, 
we  should  have  preserved  its  effigy,  or  a  sort  of  silhouette,  its 
geometric  form  upon  a  foundation  of  empty  space?  We  should 
obtain  thus  a  portion  of  space,  which  I  will  call  an  empty 
atom,  in  contrast  with  the  full  atom  which  was  there  before. 

Now  I  ask  the  atomists  to  explain  what  distinguishes  the 
full  atom  from  the  empty  one,  what  are  the  characteristics  that 
-may  be  found  in  one  and  not  in  the  other.  Is  it  the  being 
extended?  No,  for  the  empty  atom  is  extended  like  the  full 
atom.  Is  it  the  having  a  form?  No,  for  the  empty  atom  has 
a  form  as  has  the  full  atom  and  exactly  the  same  form.  Is 
it  the  being  indivisible?  No,  for  it  is  still  more  difficult  to 
understand  the  divisibility  of  space  than  of  the  body.  In  a 
word  everything  which  depends  on  extension  is  the  same  in 
the  empty  atom  as  in  the  full  atom.  But  the  empty  atom  is 
not  a  body  and  contains  nothing  corporeal ;  therefore  extension 
is  not  the  essence  of  bodies  and  perhaps  does  not  constitute  a 
part  of  this  essence.  May  we  say  that  it  is  the  motion  which 
distinguishes  the  full  atom  from  the  empty  atom?  But  before 
beginning  to  move  the  atom  must  have  already  been  some- 
thing, because  that  which  is  nothing  in  itself  can  be  neither  at 
rest,  nor  in  motion.  Motion,  therefore,  is  a  dependent  and 
subordinate  phenomenon  which  already  presupposes  a  defined 
essence.  If  we  examine  carefully  we  will  see  that  what  really 
distinguishes  the  full  atom  from  the  empty  atom  is  its  solidity 
or  weight.  Neither  solidity  nor  weight,  however,  are  modifica- 
tions of  extension ;  both  come  from  force.  It  is  accordingly, 
force  and  not  extension  which  constitutes  the  essence  of  the 
body. 

Turning  now  to  those  who,  like  the  Cartesians,  are  unwill- 


INTRODUCTION.  XVII 

ing  to  admit  the  "possibility  of  a  vacuum  and  maintain  that  all 
space  is  full,  the  demonstration  is  still  more  simple,  for  we  may 
ask  in  what  filled  space,  taken  in  its  entirety,  differs  from 
empty  space  taken  in  its  entirety.  Both  are  infinite;  both  are 
ideally  divisible  and  both  are  really  indivisible ;  both  are  sus- 
ceptible of  modalities  in  form  or  of  geometrically  defined  forms. 
Perhaps  it  will  be  claimed  that  in  full  space  the  particles  are 
movable  and  can  supplant  one  another;  in  this  case  we  are 
back  in  the  preceding  line  of  argument  and  we  shall  ask  in 
what  these  movable  particles  are  distinguished  from  the 
immovable  particles  of  space  among  which  they  move.  Thus 
the  Cartesians,  like  the  atomists,  will  be  obliged  to  recognize 
that  the  plenum  is  distinguished  from  the  vacuum  only  by 
resistance,  solidity,  motion,  activity,  in  a  word,  force. 

To  those  who  reproach  the  Leibnizian  conception  with 
idealizing  matter  too  much,  it  may  be  replied  that  matter 
taken  in  itself  is  necessarily  ideal  and  super-sensible.  Of 
course  it  cannot  be  said  that  a  body  is  only  an  assembly  of 
subjective  modifications.  The  Berkeleyan  idealism  is  a  super- 
ficial idealism,  which  will  not  stand  examination;  for  when  I 
shall  have  reduced  the  whole  universe  to  a  dream  of  my  mind 
and  to  an  expansion  of  myself  the  question  will  still  remain 
whence  comes  this  my  dream  and  what  are  the  causes  which 
have  produced  in  me  so  complicated  a  hallucination;  these 
causes  are  outside  of  me  and  they  go  beyond  me  on  every 
side ;  it. would  therefore  be  very  inappropriate  for  me  to  call  them 
myself,  for  the  I  is  strictly  that  of  which  I  have  consciousness. 
The  Fichtean  Ich,  which  by  reaction  against  itself  thus  pro- 
duces the  nicht-ich  is  only  a  complicated  and  artificial  circum- 
locution for  saying  in  a  paradoxical  form  that  there  is  a  not-I. 
At  most,  we  can  conjecture  with  the  absolute  idealism  that 
the  I  and  the  not-I  are  only  two  faces  of  one  and  the  same 
being,  which  involves  them  both  in  an  infinite  activity;  but 
we  thus  reach  a  position  very  far  from  the  idealism  of  Berkeley. 

To  return  to  the  idealism  of  Leibniz,  I  think  it  can  be  shown 
a  priori  that  matter  taken  in  itself  is  something  ideal  and 
super-sensible,  at  least  to  those  who  admit  a  divine  intelligence. 
For  it  will  readily  be  granted  that  God  does  not  know  matter 
by  means  of  the  senses ;  for  it  is  an  axiom  in  metaphysics  that 
God  has  no  senses  and  consequently  cannot  have  sensations. 
Thus:  God  can  be  neither  warm  nor  cold;  he  cannot  smell  the 


XVIII  INTRODUCTION. 

odor  of  flowers ;  he  cannot  hear'sounds,  he  cannot  see  colors ; 
he  cannot  feel  electrical  disturbances,  etc.  In  a  word,  since  he 
is  a  pure  intelligence  he  can  conceive  only  the  purely  intelligi- 
ble ;  not  that  he  is  ignorant  of  any  of  the  phenomena  of  nature, 
only  that  he  knows  them  in  their  intelligible  reasons  and  not 
through  their  sensible  impressions,  by  means  of  which  creatures 
are  aware  of  them.  Sensibility  supposes  a  subject  with  senses, 
organs  and  nerves,  that  is,  it  is  a  relation  between  created 
things.  From  God's  point  of  view,  therefore,  matter  is  not 
sensible;  it  is,  as  the  Germans  say,  ubersinnlich.  The  con- 
clusion is  easy  to  draw,  namely,  that  God,  being  absolute 
intelligence,  necessarily  sees  things  as  they  are,  and  con- 
versely the  things  in  themselves  are  such  as  he  sees  them. 
Matter  is,  accordingly,  such  in  itself  as  God  sees  it,  but  he 
sees  it  only  in  its  ideal  and  intelligible  essence ;  whence  we 
see  that  matter  is  an  intelligible  something  and  not  something 
sensible. 

To  be  sure  we  may  not  conclude  from  this  point  that  the 
essence  of  matter  does  not  consist  in  extension,  for  it  could  be 
maintained  that  extension  is  an  object  of  pure  intelligence 
quite  as  well  as  force.  But  without  taking  up  the  difficulty 
of  disengaging  extension  from  every  sensible  element,  I  wish 
to  establish  only  one  thing,  namely  that  Leibniz  cannot  [be 
reproached  with  idealizing  matter,  since  this  must  be  done  in 
every  system,  at  least  in  those  which  admit  a  divine  logos  and 
a  foreordaining  reason. 

One  of  the  most  widely  spread  objections  against  the 
monadological  system  is  the  impossibilty  of  composing  an 
extended  whole  out  of  non-extended  elements.  This  is  Euler's 
principal  objection  in  one  of  his  Letters  to  a  German  Princess 
and  he  considered  it  absolutely  definitive  because  the  necessary 
consequence  of  such  a  system  would  be  to  deny  the  reality  of 
extension  and  of  space,  and  to  launch  out  thus  into  all  the 
difficulties  of  the  idealistic  labyrinth.  I  think,  however,  that 
Euler's  objection  is  not  at  all  insoluble,  and  that  it  is  even 
possible  to  separate  the  system  of  monads  from  the  system  of 
the  ideality  of  space.  It  can  be  shown  that  all  the  questions 
relating  to  space  can  be  adjourned  or  kept  back  without  com- 
promising the  hypothesis  of  the  monads. 

For,  let  us  suppose  with  the  atomists,  with  Clarke  and 
Newton,  the  reality  of  space,  vacuums,  and  atoms.  It  is  no 


INTRODUCTION.  XIX 

more  difficult  to  conceive  of  monads  in  space  than  of  atoms ;  a 
point  of  indivisible  activity  might  be  at  a  certain  point  of  space 
and  a  collection  of  the  points  of  activity  would  constitute  the 
mass  which  we  call  a  body.  Now,  even  if  we  grant  that  these 
points  of  activity  are  separated  by  space,  yet  when  they  were 
taken  together  they  might  produce  upon  the  senses  the 
impression  of  continuous  space.  Even  in  the  case  of  what  is 
called  a  body,  say  a  marble  table,  every  one  knows  that  there 
are  forces,  that  is  to  say,  vacuums,  between  the  parts.  Since 
these  vacuums,  however,  escape  our  sense  organs,  the  body 
appears  to  us  to  be  continuous,  like  the  circle  described  by  a 
moving  succession  of  luminous  points.  In  fact  the  bodies 
would  be  composed,  as  the  Pythagoreans  have  already  said,  of 
two  elements;  the  intervals  (Stcurri^iaTa)  and  the  monads 
(nbvadet) ;  except  that  the  Pythagorean  monads  were  mere 
geometric  points,  while  for  Leibniz  they  are  active  points, 
radiating  centers  of  activity,  energies. 

Regarding  the  difficulty  of  admitting  into  space  forces  non- 
extended  and  consequently  having  no  relation  to  space,  I  grant 
that  it  is  very  serious.  It  cannot  be  raised,  however,  b/  those 
who  consider  the  soul  as  a  non-extended  force  and  as  an  indi- 
vidual substance ;  for  they  are  obliged  to  recognize  that  it  is 
in  space  although  in  its  essence  it  has  no  relation  to  space; 
there  is,  therefore,  for  them  no  contradiction  in  holding  that  a 
simple  force  is  in  space.  If,  on  the  other  hand,  it  be  denied 
that  the  soul  is  in  space,  that  it  is  in  the  body,  and  even 
that  it  is  in  a  certain  part  of  the  body,  is  it  not  clear  that  this 
would  be  attributing  to  the  soul  a  character  which  is  true  only 
of  God?  To  be  sure,  those  who  consider  the  soul  as  a  divine 
idea,  an  eternal  form  temporarily  united  to  an  individual, 
might  speak  thus.  Thus  regarded,  with  the  idealists  or  with 
Spinoza,  the  soul  is  not  in  space.  But  if  the  soul  is  represented 
as  an  individual  and  created  substance,  how  can  it  be  thought 
of  except  as  in  space  and  in  the  body  to  which  it  is  united? 
Still  more,  therefore,  in  the  case  of  monads  will  we  be  obliged 
to  admit  that  they  may  be  in  space  and  then,  as  we  have  seen, 
the  appearance  of  extension  is  explained  without  difficulty. 

If,  now,  instead  of  admitting  the  reality  of  space  we  hold 
with  Leibniz  or  with  Kant  that  it  is  ideal,  the  system  of 
monads  offers  no  longer  any  serious  difficulty,  except  from  the 
point  of  view  of  those  who  deny  the  plurality  of  individual 


XX  INTRODUCTION. 

substances.  In  any  case  Euler's  objection  evidently  loses  its 
force. 

Another  difficulty  raised  against  the  monadology  is  that  it 
effaces  the  distinction  between  the  soul  and  the  body.  This 
difficulty  seems  to  me  like  the  preceding  one  to  be  merely 
apparent.  Because  in  every  hypothesis,  the  essential  distinc- 
tion between  the  body  and  the  soul  is  that  the  body  is  a  com- 
posite, while  the  soul  is  simple.  In  order  to  prove  that  the 
soul  is  not  extended  the  proof  is  offered  that  it  is  not  a  com- 
posite, while  the  body  on  the  contrary  is.  Now  in  Leibniz's 
hypothesis  also,  the  body  is  only  a  composite,  only  an  aggrega- 
tion of  simple  elements.  What  difference  does  the  nature  of 
the  elements  make  in  this  case?  It  is  the  whole,  it  is  the 
aggregation  which  we  contrast  with  the  soul ;  and  in  Leibniz's 
hypothesis,  quite  as  well  as  in  that  of  Descartes,  the  body  as 
an  aggregation  is  wholly  incapable  of  thought. 

Some  one  will  reply:  "granting  all  that,  the  elements  are 
nevertheless  single  and  indivisible  like  the  soul  itself  and  they 
are  therefore  of  the  same  nature  as  the  soul — they  are  souls 
themselves. ' '  This  last  consequence  is  very  incorrectly  drawn, 
however. 

What  is  meant  by  the  words :  "of  the  same  nature"?  Does 
it  mean  that  the  monads  which  compose  the  body  are  feeling, 
thinking,  willing  beings?  Leibniz  never  said  such  a  thing. 
What  is  the  basis  for  affirming  that  the  particles  of  my  body 
are  thinking  substances?  Let  us  look  at  the  semblance  they 
have  to  the  soul.  Doubtless  they  are  like  it  single  and  indivisi- 
ble substances.  But  what  difficulty  does  it  introduce  to  admit 
that  the  soul  and  body  have  common  attributes?  The  atoms, 
for  instance,  have  they  not  in  common  with  the  soul,  existence, 
indestructibility,  self -identity?  And  does  the  argument  of  the 
identity  of  the  ego  in  contrast  with  the  changing  nature  of 
organized  matter,  cease  to  be  valid,  because  the  atom  is  quite 
as  self-identical  as  the  soul?  Indeed  the  indestructibility  of 
the  atom  is  used  as  an  analogy  to  establish  the  indestructi- 
bility of  the  soul.  If  this  common  character  does  not  prevent 
their  being  distinguished,  why  should  their  being  distinguished 
be  more  difficult  when  they  have  in  common  a  character  essen- 
tial to  all  substance,  namely,  the  attribute  of  activity? 

Furthermore,  if  the  atoms  of  the  substance,  which  constitutes 
the  universe,  are  indivisible  units,  the  power  of  thinking  is  not 


INTRODUCTION.  XXI 

inconsistent  with  their  conception.  They  may  be  thinking 
substances,  and  it  cannot  be  denied  that  in  this  system  a 
monad  may  become,  if  God  wishes  it,  a  thinking  soul.  If  on 
the  one  hand  it  is  not  impossible,  there  is  no  way,  on  the  other 
hand,  of  proving  that  it  may  be  so.  Why  may  there  not  be 
several  orders  of  monads  which  are  unable  to  pass  from  one 
class  to  another?  Why  may  there  not  be  monads  having 
merely  mechanical  properties ;  others  of  a  higher  order,  con- 
taining the  principle  of  life,  like  plant  souls ;  still  higher  sen- 
sitive souls;  and  finally  free  and  intelligent  souls  endowed 
with  personality  and  immortality?  Leibniz's  system  is  no  more 
opposed  than  any  other  to  these  orders. 

If,  however,  by  a  bolder  hypothesis,  the  possibility  of  a 
monad's  passing  from  one  order  to  another  be  admitted,  there 
would  still  be  nothing  here  degrading  to  the  true  dignity  of 
man,  for,  after  all  it  must  be  recognized  that  the  human  soul 
in  its  first  state  is  hardly  anything  more  than  a  plant-soul 
which  lifts  itself  by  degrees  to  the  condition  of  a  thinking  soul. 
Therefore  there  will  be  no  contradiction  in  admitting  that 
every  monad  contains  potentially  a  thinking  soul.  Should 
such  a  hypothesis  be  repugnant,  I  still  maintain  that  the  mon- 
adological  system  does  not  force  one  to  it,  since  monadism 
quite  as  well  as  the  popular  atomism  can  admit  a  scale  of 
substances  essentially  distinct  from  one  another. 

Another  objection  which  the  Leibnizian  excites,  and  one 
which  Arnauld  does  not  fail  to  raise  in  one  of  his  letters,  is 
that  the  system  of  monads  weakens  the  argument  of  a  first 
mover,  since  it  implies  that  matter  can  be  endowed  with 
active  force  and  consequently  with  spontaneous  motion. 
Leibniz  does  not  meet  this  objection  in  a  convincing  manner 
and  says  merely  that  recourse  must  be  had  to  God  to  explain 
the  co-ordination  of  movements.  This,  however,  avoids  the 
point,  for  the  co-ordination  has  no  relation  to  the  argument  of 
the  first  mover,  only  to  that  of  the  ordering  and  of  the  arrange- 
ment which  is  a  wholly  different  matter.  We  may,  however, 
remark  that  Leibniz,  in  order  •  to  establish  the  reality  of  the 
force  in  corporeal  substance,  much  more  frequently  uses  the 
fact  of  resistance  to  motion,  than  that  of  the  so-called  spon- 
taneous motion.  For  instance,  one  of  his  principal  arguments 
is  that  a  moving  body,  when  it  comes  in  contact  with  another, 
loses  motion  in  proportion  to  the  resistance  which  the  other 


XXII  INTRODUCTION. 

opposes  to  it,  and  this  is  what  he  calls  inertia.  It  is  evi- 
dent, therefore  that  if  a  substance  in  repose  reveals  itself  by 
its  resistance  to  motion,  the  argument  of  the  first  mover,  far 
from  being  weakened  is,  on  the  contrary,  strengthened. 

Besides  this,  even  if  a  spontaneous  disposition  to  movement, 
be  admitted  in  the  elements  of  bodies,  yet  experience  compels 
us  to  recognize  that  this  disposition  passes  over  into  action  only 
upon  the  excitation  of  an  exterior  action  because  we  never  see 
a  body  put  in  motion  except  in  the  presence  of  another.  The 
actual  indifference  to  movement  and  to  repose,  which  at  the 
present  time  is  called,  in  mechanics,  inertia,  must  always  be 
admitted,  whether  we  posit  in  the  body  a  virtual  disposition  to 
movement  or  whether,  on  the  contrary,  the  body  be  considered 
as  absolutely  passive ;  in  either  case  there  must  be  a  cause  deter- 
mining the  motion ;  it  is  not  necessary  that  this  first  cause  pro- 
duce everything  in  the  body  moved,  and  that  it  should  be  in 
some  sort  the  total  cause  of  the  motion ;  sufficient  is  it  for  it  to  be 
the  complementary  cause  as  the  Schoolmen  used  to  say. 

Furthermore  inertia  must  not  be  confounded  with  absolute 
inactivity.  Leibniz  showed  admirably  that  an  absolutely 
passive  substance  would  be  a  pure  nothing;  that  a  being  is 
active  in  proportion  as  it  is  in  existence;  in  a  word,  that  to 
be  and  to  act  are  one  and  the  same  thing.  From  the  fact, 
however,  that  a  substance  is  essentially  active,  it  does  not  nee. 
essarily  follow  that  it  is  endowed  with  spontaneous  motion,  for 
th  e  latter  is  only  a  special  mode  of  activity  and  is  not  the  only 
one.  For  example,  resistance,  or  impenetrability,  is  a  certain 
kind  of  activity,  but  is  not  motion.  They  are  mistaken,  there- 
fore, who  think  that  the  theory  of  active  matter  does  away 
with  a  first  cause  for  motion,  because  even  if  motion  be  essential 
to  matter,  we  will  still  have  to  explain  why  no  portion  of  mat- 
ter is  ever  spontaneously  in  motion. 

In  short,  according  to  Leibniz,  every  being  is  essentially 
active.  That  which  does  not  act  does  not  exist ;  quid  non 
agtt  non  existit.  Now,  whatever  acts  is  force ;  therefore,  every- 
thing is  force  or  a  compound  of  forces.  The  essence  of  matter 
is  not,  as  Descartes  thought,  inert  extension,  it  is  action,  effort, 
energy.  Furthermore  the  body  is  a  compound  and  the  com* 
pound  presupposes  a  simple.  The  forces,  therefore,  which 
compose  the  body  are  simple  elements,  unextended — incor- 
poreal atoms.  Thus  the  universe  is  a  vast  dynamism,  a  wise 


INTRODUCTION.  XXIII 

system  of  individual  forces,  harmoniously  related  under  the 
direction  of  a  primordial  force,  whose  absolute  activity  permits 
the  existence  outside  of  itself  of  the  appropriate  activities  of 
created  things,  which  it  directs  without  absorbing  them.  This 
system,  therefore,  may  be  reduced  to  three  principal  points: 
i,  it  makes  the  idea  of  force  predominate  over  the  idea  of  sub- 
stance, or  rather  reduces  substance  to  force;  2,  it  sees  in  exten- 
sion only  a  mode  of  appearance  of  force  and  compares  the 
bodies  of  simple  and  unextended  elements  as  more  or  less 
analogous,  except  in  their  degree,  to  what  is  called  the  soul ; 
3,  it  sees  in  the  forces  not  only  general  agents  or  modes  of 
action  of  a  universal  agent,  as  have  the  scientists,  but  it  sees 
also  individual  principles,  both  substances  and  causes  which  are 
inseparable  from  the  material,  or  rather  which  constitute  mat- 
ter itself;  Dynamism  thus  understood,  is  only  universal 
spiritualism. 

In  this  introduction  I  have  examined  the  different  difficul- 
ties which  might  be  raised  against  the  Leibnizian  Monadology 
from  the  point  of  view  of  the  Cartesian  spiritualism.  They 
have  still  to  be  examined  from  the  point  of  view  of  those  who 
deny  the  plurality  of  substances,  that  is,  from  the  Spinozistic 
or  pantheistic  point  of  view.  Here,  however,  come  in  a  wholly 
different  class  of  ideas,  which  we  cannot  enter  upon  without 
extending  this  introduction  beyond  measure.  We  will  merely 
say  that  the  force  of  Leibniz's  system  is  in  the  fact  of  individ- 
uality, of  which  the  advocates  of  the  unity  of  substance  have 
never  been  able  to  give  an  explanation.  It  is  true,  we  must 
pass  here  from  the  objective  to  the  subjective  standpoint, 
because  it  is  in  the  consciousness  that  the  individuality  mani- 
fests itself  in  the  most  striking  manner,  while  in  nature  it  is 
more  veiled.  One's  position,  therefore,  should  be  taken  in  the 
region  of  the  individual  consciousness  in  order  to  combat 
Spinozism.  This  point  of  view  has  been  particularly  devel- 
oped in  our  day  by  Maine  de  Biran  and  by  his  school.  We 
have  been  content  to  mention  it  merely,  not  desiring  to  skim 
over  a  problem  which  is  connected  with  the  knottiest  points  of 
metaphysics  and  of  the  philosophy  of  religion. 


METAPHYSICS. 


METAPHYSICS. 

I.  Concerning  the  divine  perfection  and  that  God 
does  everything  in  the  most  desirable  way. 

The  conception  of  God  which  is  the  most  common 
and  the  most  full  of  meaning  is  expressed  well 
enough  in  the  words:  God  is  an  absolutely  perfect 
being.  The  implications,  however,  of  these  words 
fail  to  receive  sufficient  consideration.  For  in- 
stance, there  are  many  different  kinds  of  perfection, 
all  of  which  God  possesses,  and  each  one  of  them 
pertains  to  him  in  the  highest  degree. 

We  must  also  know  what  perfection  is.  One 
thing  which  can  surely  be  affirmed  about  it  is  that 
those  forms  or  natures  which  are  not  susceptible  of 
it  to  the  highest  degree,  say  the  nature  of  numbers 
or  of  figures,  do  not  permit  of  perfection.  This  is 
because  the  number  which  is  the  greatest  of  all  (that 
is,  the  sum  of  all  the  numbers),  and  likewise  the 
greatest  of  all  figures,  imply  contradictions.  The 
greatest  knowledge,  however,  and  omnipotence 
contain  no  impossibility.  Consequently  power  and 
knowledge  do  admit  of  perfection,  and  in  so  far  as 
they  pertain  to  God  they  have  no  limits. 

Whence  it  follows  that  God  who  possesses 
supreme  and  infinite  wisdom  acts  in  the  most  per- 
fect manner  not  only  metaphysically,  but  also  from 
the  moral  standpoint.  And  with  respect  to  our- 

3 


4  LEIBNIZ. 

selves  it  can  be  said  that  the  more  we  are 
enlightened  and  informed  in  regard  to  the  works 
of  God  the  more  will  we  be  disposed  to  find  them 
excellent  and  conforming  entirely  to  that  which  we 
might  desire. 

II.  Against  those  who  hold  that  there  is  in  the 
works  of  God  no  goodness,  or  that  the  principles  of 
goodness  and  beauty  are  arbitrary. 

Therefore  I  am  far  removed  from  the  opinion  of 
those  who  maintain  that  there  are  no  principles  of 
goodness  or  perfection  in  the  nature  of  things,  or 
in  the  ideas  which  God  has  about  them,  and  who 
say  that  the  works  of  God  are  good  only  through 
the  formal  reason  that  God  has  made  them.  If  this 
position  were  true,  God,  knowing  that  he  is  the 
author  of  things,  would  not  have  to  regard  them 
afterwards  and  find  them  good,  as  the  Holy  Scrip- 
ture witnesses.  Such  anthropological  expressions 
are  used  only  to  let  us  know  that  excellence  is 
recognized  in  regarding  the  works  themselves,  even 
if  we  do  not  consider  their  evident  dependence  on 
their  author.  This  is  confirmed  by  the  fact  that  it 
is  in  reflecting  upon  the  works  that  we  are  able  to 
discover  the  one  who  wrought.  They  must  there- 
fore bear  in  themselves  his  character.  I  confess 
that  the  contrary  opinion  seems  to  me  extremely 
dangerous  and  closely  approaches  that  of  recent 
innovators  who  hold  that  the  beauty  of  the  universe 
and  the  goodness  which  we  attribute  to  the  works 
of  God  are  chimeras  of  human  beings  who  think 
of  God  in  human  terms.  In  saying,  therefore,  that 
things  are  not  good  according  to  any  standard  of 
goodness,  but  simply  by  the  will  of  God,  it  seems 


DISCOURSE  ON  METAPHYSICS.  5 

to  me  that  one  destroys,  without  realizing  it,  all 
the  love  of  God  and  all  his  glory;  for  why  praise 
him  for  what  he  has  done,  if  he  would  be  equally 
praiseworthy  in  doing  the  contrary?  Where  will 
be  his  justice  and  his  wisdom  if  he  has  only  a  cer- 
tain despotic  power,  if  arbitrary  will  takes  the  place 
of  reasonableness,  and  if  in  accord  with  the  defini- 
tion of  tyrants,  justice  consists  in  that  which  is 
pleasing  to  the  most  powerful?  Besides  it  seems 
that  every  act  of  willing  supposes  some  reason  for 
the  willing  and  this  reason,  of  course,  must  precede 
the  act.  This  is  why,  accordingly,  I  find  so  strange 
those  expressions  of  certain  philosophers  who  say 
that  the  eternal  truths  of  metaphysics  and  Geometry, 
and  consequently  the  principles  of  goodness,  of 
justice,  and  of  perfection,  are  effects  only  of  the  will 
of  God.  To  me  it  seems  that  all  these  follow  from 
his  understanding,  which  does  not  depend  upon  his 
will  any  more  than  does  his  essence. 

III.  Against  those  who  think  that  God  might  have 
made  things  better  than  he  has. 

No  more  am  I  able  to  approve  of  the  opinion  of 
certain  modern  writers  who  boldly  maintain  that 
that  which  God  has  made  is  not  perfect  in  the 
highest  degree,  and  that  he  might  have  done  better. 
It  seems  to  me  that  the  consequences  of  such  an 
opinion  are  wholly  inconsistent  with  the  glory  of 
God.  Uti  minus  malum  habet  rationem  boni,  ita 
minus  bonum  habet  rationem  mali.  I  think  that  one 
acts  imperfectly  if  he  acts  with  less  perfection 
than  he  is  capable  of.  To  show  that  an  architect 
could  have  done  better  is  to  find  fault  with  his 
work.  Furthermore  this  opinion  is  contrary  to  the 


6  LEIBNIZ. 

Holy  Scriptures  when  they  assure  us  of  the  good- 
ness of  God's  work.  For  if  comparative  perfection 
were  sufficient,  then  in  whatever  way  God  had 
accomplished  his  work,  since  there  is  an  infinitude 
of  possible  imperfections,  it  would  always  have 
been  good  in  comparison  with  the  less  perfect;  but 
a  thing  is  little  praiseworthy  when  it  can  be  praised 
only  in  this  way. 

I  believe  that  a  great  many  passages  from  the 
divine  writings  and  from  the  holy  fathers  will  be 
found  favoring  my  position,  while  hardly  any  will 
be  found  in  favor  of  that  of  these  modern  thinkers. 
Their  opinion  is,  in  my  judgment,  unknown  to  the 
writers  of  antiquity  and  is  a  deduction  based  upon 
the  too  slight  acquaintaince  which  we  have  with 
the  general  harmony  of  the  universe  and  with  the 
hidden  reasons  for  God's  conduct.  In  our  igno- 
rance, therefore,  we  are  tempted  to  decide  auda- 
ciously that  many  things  might  have  been  done 
better. 

These  modern  thinkers  insist  upon  certain  hardly 
tenable  subtleties,  for  they  imagine  that  nothing  is 
so  perfect  that  there  might  not  have  been  something 
more  perfect.  This  is  an  error.  They  think, 
indeed,  that  they  are  thus  safeguarding  the  liberty 
of  God.  As  if  it  were  not  the  highest  liberty  to 
act  in  perfection  according  to  the  sovereign  reason. 
For  to  think  that  God  acts  in  anything  without  hav- 
ing any  reason  for  his  willing,  even  if  we  overlook 
the  fact  that  such  action  seems  impossible,  is  an 
opinion  which  conforms  little  to  God's  glory.  For 
example,  let  us  suppose  that  God  chooses  between 
A  and  B,  and  that  he  takes  A  without  any  reason 
for  preferring  it  to  B.  I  say  that  this  action  on  the 


DISCOURSE    ON    METAPHYSICS.  ^ 

part  of  God  is  at  least  not  praiseworthy,  for  all 
praise  ought  to  be  founded  upon  reason  which  ex 
hypothesi  is  not  present  here.  My  opinion  is  that 
God  does  nothing  for  which  he  does  not  deserve  to 
be  glorified 

IV.  That  love  for  God  demands  on  our  part  complete 
satisfaction  with  and  acquiescence  in  that  which  he  has 
done. 

The  general  knowledge  of  this  great  truth  that 
God  acts  always  in  the  most  perfect  and  most 
desirable  manner  possible,  is  in  my  opinion  the  basis 
of  the  love  which  we  owe  to  God  in  all  things;  for 
he  who  loves  seeks  his  satisfaction  in  the  felicity 
or  perfection  of  the  object  loved  and  in  the  perfec- 
tion of  his  actions.  Idem  velle  et  idem  nolle  vera 
amicitia  est.  I  believe  that  it  is  difficult  to  love 
God  truly  when  one,  having  the  power  to  change 
his  disposition,  is  not  disposed  to  wish  for  that 
which  God  desires.  In  fact  those  who  are  not 
satisfied  with  what  God  does  seem  to  me  like  dis- 
satisfied subjects  whose  attitude  is  not  very  differ- 
ent from  that  of  rebels.  I  hold  therefore,  that  on 
these  principles,  to  act  conformably  to  the  love  of 
God  it  is  not  sufficient  to  force  oneself  to  be  patient, 
we  must  be  really  satisfied  with  all  that  comes  to 
us  according  to  his  will.  I  mean  this  acquiescence 
in  regard  to  the  past;  for  as  regards  the  future  one 
should  not  be  a  quietist  with  the  arms  folded, 
open  to  ridicule,  awaiting  that  which  God  will  do; 
according  to  the  sophism  which  the  ancients  called 
Ao'yov  atpyov,  the  lazy  reason.  It  is  necessary  to  act 
conformably  to  the  presumptive  will  of  God  as 
far  as  we  are  able  to  judge  of  it,  trying  with  all  our 


8  LEIBNIZ. 

might  to  contribute  to  the  general  welfare  and  par- 
ticularly to  the  ornamentation  and  the  perfection  of 
that  which  touches  us,  or  of  that  which  is  nigh  and 
so  to  speak  at  our  hand.  For  if  the  future  shall 
perhaps  show  that  God  has  not  wished  our  good 
intention  to  have  its  way,  it  does  not  follow  that 
he  has  not  wished  us  to  act  as  we  have;  on  the  con- 
trary, since  he  is  the  best  of  all  masters,  he  ever 
demands  only  the  right  intentions,  and  it  is  for  him 
to  know  the  hour  and  the  proper  place  to  let  good 
designs  succeed. 

V.  In  what  the  principles  of  the  divine  perfection 
consist,  and  that  the  simplicity  of  the  means  counter- 
balances the  richness  of  the  effects. 

It  is  sufficient  therefore  to  have  this  confidence  in 
God,  that  he  has  done  everything  for  the  best  and 
that  nothing  will  be  able  to  injure  those  who  love 
him.  To  know  in  particular,  however,  the  reasons 
which  have  moved  him  to  choose  this  order  of  the 
universe,  to  permit  sin,  to  dispense  his  salutary 
grace  in  a  certain  manner, — this  passes  the  capacity 
of  a  finite  mind,  above  all  when  such  a  mind  has 
not  come  into  the  joy  of  the  vision  of  God.  Yet  it 
is  possible  to  make  some  general  remarks  touching 
the  course  of  providence  in  the  government  of 
things.  One  is  able  to  say,  therefore,  that  he  who 
acts  perfectly  is  like  an  excellent  Geometer  who 
knows  how  to  find  the  best  construction  for  a  prob- 
•lem;  like  a  good  architect  who  utilizes  his  location 
and  the  funds  destined  for  the  building  in  the 
most  advantageous  manner,  leaving  nothing  which 
shocks  or  which  does  not  display  that  beauty  of 


DISCOURSE    ON    METAPHYSICS.  9 

which  it  is  capable;  like  a  good  householder  who 
employs  his  property  in  such  a  way  that  there  shall 
be  nothing  uncultivated  or  sterile;  like  a  clever 
machinist  who  makes  his  production  in  the  least 
difficult  way  possible;  and  like  an  intelligent  author 
who  encloses  the  most  of  reality  in  the  least  possi- 
ble compass. 

Of  all  beings  those  which  are  the  most  perfect  and 
occupy  the  least  possible  space,  that  is  to  say  those 
which  interfere  with  one  another  the  least,  are  the 
spirits  whose  perfections  are  the  virtues.  That  is 
why  we  may  not  doubt  that  the  felicity  of  the  spirits 
is  the  principal  aim  of  God  and  that  he  puts  this 
purpose  into  execution,  as  far  as  the  general  har- 
mony will  permit.  We  will  recur  to  this  subject 
again. 

When  the  simplicity  of  God's  way  is  spoken  of, 
reference  is  specially  made  to  the  means  which  he 
employs,  and  on  the  other  hand  when  the  variety, 
richness  and  abundance  are  referred  to,  the  ends  or 
effects  are  had  in  mind.  Thus  one  ought  to  be 
proportioned  to  the  other,  just  as  the  cost  of  a 
building  should  balance  the  beauty  and  grandeur 
which  is  expected.  It  is  true  that  nothing  costs 
God  anything,  just  as  there  is  no  cost  for  a  philos- 
opher who  makes  hypotheses  in  constructing  his 
imaginary  world,  because  God  has  only  to  make 
decrees  in  order  that  a  real  world  come  into  being; 
but  in  matters  of  wisdom  the  decrees  or  hypotheses 
meet  the  expenditure  in  proportion  as  they  are 
more  independent  of  one  another.  The  reason 
wishes  to  avoid  multiplicity  in  hypotheses  or  prin- 
ciples very  much  as  the  simplest  system  is  preferred 
in  Astronomy. 


10  LEIBNIZ. 

VI.  That  God  does  nothing  which  is  not  orderly,  and 
that  it  is  not  even  possible  to  conceive  of  events  which 
are  not  regular. 

The  activities  or  the  acts  of  will  of  God  are  com- 
monly divided  into  ordinary  and  extraordinary. 
But  it  is  well  to  bear  in  mind  that  God  does  nothing 
out  of  order.  Therefore,  that  which  passes  for 
extraordinary  is  so  only  with  regard  to  a  particular 
order  established  among  the  created  things,  for  as 
regards  the  universal  order,  everything  conforms  to 
it.  This  is  so  true  that  not  only  does  nothing  occur 
in  this  world  which  is  absolutely  irregular,  but 
it  is  even  impossible  to  conceive  of  such  an  occur- 
rence. Because,  let  us  suppose  for  example  that  some 
one  jots  down  a  quantity  of  points  upon  a  sheet  of 
paper  helter  skelter,  as  do  those  who  exercise  the 
ridiculous  art  of  Geomancy;  now  I  say  that  it  is 
possible  to  find  a  geometrical  line  whose  concept 
shall  be  uniform  and  constant,  that  is,  in  accordance 
with  a  certain  formula,  and  which  line  at  the  same 
time  shall  pass  through  all  of  those  points,  and 
in  the  same  order  in  which  the  hand  jotted  them 
down;  also  if  a  continuous  line  be  traced,  which  is 
now  straight,  now  circular,  and  now  of  any  other 
description,  it  is  possible  to  find  a  mental  equiva- 
lent, a  formula  or  an  equation  common  to  all  the 
points  of  this  line  by  virtue  of  which  formula  the 
changes  in  the  direction  of  the  line  must  occur. 
There  is  no  instance  of  a  face  whose  contour  does 
not  form  part  of  a  geometric  line  and  which  can  not 
be  traced  entire  by  a  certain  mathematical  motion. 
But  when  the  formula  is  very  complex,  that  which 
conforms  to  it  passes  for  irregular.  Thus  we  may 


DISCOURSE    ON    METAPHYSICS.  II 

say  that  in  whatever  manner  God  might  have 
created  the  world,  it  would  always  have  been  regu- 
lar and  in  a  certain  order.  God,  however,  has 
chosen  the  most  perfect,  that  is  to  say  the  one 
which  is  at  the  same  time  the  simplest  in  hypotheses 
and  the  richest  in  phenomena,  as  might  be  the  case 
with  a  geometric  line,  whose  construction  was  easy, 
but  whose  properties  and  effects  were  extremely 
remarkable  and  of  great  significance.  I  use  these 
comparisons  to  picture  a  certain  imperfect  resem- 
blance to  the  divine  wisdom,  and  to  point  out  that 
which  may  at  least  raise  our  minds  to  conceive  in 
some  sort  what  cannot  otherwise  be  expressed.  I 
do  not  pretend  at  all  to  explain  thus  the  great  mys- 
tery upon  which  depends  the  whole  universe. 

VII.  That  miracles  conform  to  the  regular  order 
although  they  go  against  the  subordinate  regulations; 
concerning  that  which  God  desires  or  permits  and  con- 
cerning general  and  particular  intentions. 

Now  since  nothing  is  done  which  is  not  orderly, 
we  may  say  that  miracles  are  quite  within  the  order 
of  natural  operations.  We  use  the  term  natural  of 
these  operations  because  they  conform  to  certain 
subordinate  regulations  which  we  call  the  nature  of 
things.  For  it  can  be  said  that  this  nature  is  only 
a  custom  of  God's  which  he  can  change  on  the 
occasion  of  a  stronger  reason  than  that  which 
moved  him  to  use  these  regulations.  As  regards 
general  and  particular  intentions,  according  to  the 
way  in  which  we  understand  the  matter,  it  may  be 
said  on  the  one  hand  that  everything  is  in  accor- 
dance with  his  most  general  intention,  or  that  which 
best  conforms  to  the  most  perfect  order  he  has 


12  LEIBNIZ. 

chosen;  on  the  other  hand,  however,  it  is  also  pos- 
sible to  say  that  he  has  particular  intentions  which 
are  exceptions  to  the  subordinate  regulations  above 
mentioned.  Of  God's  laws,  however,  the  most 
universal,  i.  e.,  that  which  rules  the  whole  course 
of  the  universe,  is  without  exceptions. 

It  is  possible  to  say  that  God  desires  everything 
which  is  an  object  of  his  particular  intention. 
When  we  consider  the  objects  of  his  general  inten- 
tions, however,  such  as  are  the  modes  of  activities 
of  created  things  and  especially  of  the  reasoning 
creatures  with  whom  God  wishes  to  co-operate,  we 
must  make  a  distinction;  for  if  the  action  is  good 
in  itself,  we  may  say  that  God  wishes  it  and  at 
times  commands  it,  even  though  it  does  not  take 
place;  but  if  it  is  bad  in  itself  and  becomes 
good  only  by  accident  through  the  course  of  events 
and  especially  after  chastisement  and  satisfaction 
have  corrected  its  malignity  and  rewarded  the  ill 
with  interest  in  such  a  way  that  more  perfection 
results  in  the  whole  train  of  circumstances  than 
would  have  come  if  that  ill  had  not  occurred, — if 
all  this  takes  place  we  must  say  that  God  permits 
the  evil,  and  not  that  he  desired  it,  although  he  has 
co-operated  by  means  of  the  laws  of  nature  which 
he  has  established.  He  knows  how  to  produce  the 
greatest  good  from  them. 

VIII.  In  order  to  distinguish  between  the  activities 
of  God  and  the  activities  of  created  things  we  must 
explain  the  conception  of  an  individual  substance. 

It  is  quite  difficult  to  distinguish  God's  actions 
from  those  of  his  creatures.  Some  think  that  God 
does  everything;  others  imagine  that  he  only  con- 


DISCOURSE    ON    METAPHYSICS.  13 

serves  the  force  that  he  has  given  to  created  things. 
How  far  can  we  say  either  of  these  opinions  is  right? 
In  the  first  place  since  activity  and  passivity  per- 
tain properly  to  individual  substances  (actiones  sunt 
suppositonini}  it  will  be  necessary  to  explain  what 
such  a  substance  is.  It  is  indeed  true  that  when 
several  predicates  are  attributes  of  a  single  subject 
and  this  subject  is  not  an  attribute  of  another,  we 
speak  of  it  as  an  individual  substance,  but  this  is  not 
enough,  and  such  an  explanation  is  merely  nom- 
inal. We  must  therefore  inquire  what  it  is  to  be  an 
attribute  in  reality  of  a  certain  subject.  Now  it  is 
evident  that  every  true  predication  has  some  basis 
in  the  nature  of  things,  and  even  when  a  proposition 
is  not  identical,  that  is,  when  the  predicate  is  not 
expressly  contained  in  the  subject,  it  is  still  neces- 
sary that  it  be  virtually  contained  in  it,  and  this  is 
what  the  philosophers  call  in-esse,  saying  thereby 
that  the  predicate  is  in  the  subject.  Thus  the  con- 
tent of  the  subject  must  always  include  that  of  the 
predicate  in  such  a  way  that  if  one  understands 
perfectly  the  concept  of  the  subject,  he  will  know 
that  the  predicate  appertains  to  it  also.  This  being 
so,  we  are  able  to  say  that  this  is  the  nature  of  an 
individual  substance  or  of  a  complete  being,  namely, 
to  afford  a  conception  so  complete  that  the  concept 
shall  be  sufficient  for  the  understanding  of  it  and 
for  the  deduction  of  all  the  predicates  of  which  the 
substance  is  or  may  become  the  subject.  Thus  the 
quality  of  king,  which  belonged  to  Alexander  the 
Great,  an  abstraction  from  the  subject,  is  not  suffi- 
ciently determined  to  constitute  an  individual,  and 
does  not  contain  the  other  qualities  of  the  same 
subject,  nor  everything  which  the  idea  of  this 


14  LEIBNIZ. 

prince  includes.  God,  however,  seeing  the  indi- 
vidual concept,  or  haecceity,  of  Alexander,  sees 
there  at  the  same  time  the  basis  and  the  reason  of 
all  the  predicates  which  can  be  truly  uttered  regard- 
ing him;  tor  instance  that  he  will  conquer  Darius 
and  Porus,  even  to  the  point  of  knowing  a  priori 
(and  not  by  experience)  whether  he  died  a  natural 
death  or  by  poison, — facts  which  we  can  learn  only 
through  history.  When  we  carefully  consider  the 
connection  of  things  we  see  also  the  possibility  of 
saying  that  there  was  always  in  the  soul  of  Alexan- 
der marks  of  all  that  had  happened  to  him  and 
evidences  of  all  that  would  happen  to  him  and 
traces  even  of  everything  which  occurs  in  the  uni- 
verse, although  God  alone  could  recognize  them  all. 

IX.  That  every  individual  substance  expresses  the 
whole  universe  in  its  own  manner  and  that  in  its  full 
concept  is  included  all  its  experiences  together  with  all 
the  attendent  circumstances  and  the  whole  sequence  of 
exterior  events. 

There  follow  from  these  considerations  several 
noticeable  paradoxes;  among  others  that  it  is  not 
true  that  two  substances  may  be  exactly  alike  and 
differ  only  numerically,  solo  mimero,  and  that  what  St. 
Thomas  says  on  this  point  regarding  angels  and 
intelligences  (quod  ibi  omne  individuum  sit  species 
infimd)  is  true  of  all  substances,  provided  that  the 
specific  difference  is  understood  as  Geometers 
understand  it  in  the  case  of  figures;  again  that 
a  substance  will  be  able  to  commence  only  through 
creation  and  perish  only  through  annihilation;  that 
a  substance  cannot  be  divided  into  two  nor  can  one 
be  made  out  of  two,  and  that  thus  the  number  of 


DISCOURSE    ON    METAPHYSICS.  15 

substances  neither  augments  nor  diminishes  through 
natural  means,  although  they  are  frequently  trans- 
formed. Furthermore  every  substance  is  like  an 
entire  world  and  like  a  mirror  of  God,  or  indeed  of 
the  whole  world  which  it  portrays,  each  one  in  its 
own  fashion;  almost  as  the  same  city  is  variously 
represented  according  to  the  various  situations  of 
him  who  is  regarding  it.  Thus  the  universe  is  mul- 
tiplied in  some  sort  as  many  times  as  there  are  sub- 
stances, and  the  glory  of  God  is  multiplied  in  the 
same  way  by  as  many  wholly  different  representa- 
tions of  his  works.  It  can  indeed  be  said  'that  every 
substance  bears  in  some  sort  the  character  of  God's 
infinite  wisdom  and  omnipotence,  and  imitates  him 
as  much  as  it  is  able  to;  for  it  expresses,  although 
confusedly,  all  that  happens  in  the  universe,  past, 
present  'and  future,  deriving  thus  a  certain  resem- 
blance to  an  infinite  perception  or  power  of  know- 
ing. And  since  all  other  substances  express  this 
particular  substance  and  accommodate  themselves  to 
it,  we  can  say  that  it  exerts  its  power  upon  all  the 
others  in  imitation  of  the  omnipotence  of  the  cre- 
ator. 

X.  That  the  belief  in  substantial  forms  has  a  cer- 
tain basis  in  fact,  but  that  these  forms  effect  no  changes 
in  the  phenomena  and  must  not  be  employed  for  the 
explanation  of  particular  events. 

It  seems  that  the  ancients,  able  men,  who  were 
accustomed  to  profound  meditations  and  taught  the- 
ology and  philosophy  tor  several  centuries  and  some 
of  whom  recommend  themselves  to  us  on  account  of 
their  piety,  had  some  knowledge  of  that  which  we 
have  just  said  and  this  is  why  they  introduced  and 


l6  LEIBNIZ. 

maintained  the  substantial  forms  so  much  decried 
to-day.  But  they  were  not  so  far  from  the  truth 
nor  so  open  to  ridicule  as  the  common  run  of  our 
new  philosophers  imagine.  I  grant  that  the  con- 
sideration of  these  forms  is  of  no  service  in  the 
details  of  physics  and  ought  not  to  be  employed  in 
the  explanation  of  particular  phenomena.  In  regard 
to  this  last  point,  the  schoolmen  were  at  fault,  as 
were  also  the  physicians  of  times  past  who  followed 
their  example,  thinking  they  had  given  the  reason 
for  the  properties  of  a  body  in  mentioning  the  forms 
and  qualities  without  going  to  the  trouble  of  exam- 
ining the  manner  of  operation;  dS  if  one  should  be 
content  to  say  that  a  clock  had  a  certain  amount 
of  clockness  derived  from  its  form,  and  should  not 
inquire  in  what  that  clockness  consisted.  This  is 
indeed  enough  for  the  man  who  buys  it,  provided 
he  surrenders  the  care  of  it  to  someone  else.  The 
fact,  however,  that  there  was  this  misunderstanding 
and  misuse  of  the  substantial  forms  should  not  bring 
us  to  throw  away  something  whose  recognition  is 
so  necessary  in  metaphysics.  Since  without  these 
we  will  not  be  able,  I  hold,  to  know  the  ultimate 
principles  nor  to  lift  our  minds  to  the  knowledge 
of  the  incorporeal  natures  and  of  the  marvels  of 
God.  Yet  as  the  geometer  does  not  need  to 
encumber  his  mind  with  the  famous  puzzle  of  the 
composition  of  the  continuum,  and  as  no  moralist, 
and  still  less  a  jurist  or  a  statesman  has  need  to 
trouble  himself  with  the  great  difficulties  which 
arise  in  conciliating  free  will  with  the  providential 
activity  of  God,  (since  the  geometer  is  able  to  make 
all  his  demonstrations  and  the  statesman  can  com- 
plete all  his  deliberations  without  entering  into 


DISCOURSE   ON    METAPHYSICS.  17 

these  discussions  which  are  so  necessary  and  impor- 
tant in  Philosophy  and  Theology),  so  in  the  same 
way  the  physicist  can  explain  his  experiments,  now 
using  simpler  experiments  already  made,  now 
employing  geometrical  and  mechanical  demonstra- 
tions without  any  need  of  the  general  considerations 
which  belong  to  another  sphere,  and  if  he  employs 
the  co-operation  of  God,  or  perhaps  of  some  soul  or 
animating  force,  or  something  else  of  a  similar 
nature,  he  goes  out  of  his  path  quite  as  much  as  that 
man  who,  when  facing  an  important  practical  ques- 
tion would  wish  to  enter  into  profound  argumenta- 
tions regarding  the  nature  of  destiny  and  of  our 
liberty;  a  fault  which  men  quite  frequently  com- 
mit without  realizing  it  when  they  cumber  their 
minds  with  considerations  regarding  fate,  and  thus 
they  are  even  sometimes  turned  from  a  good  reso- 
lution or  from  some  necessary  provision. 

XI.  That  the  opinions  of  the  theologians  and  of  the 
so-called  scholastic  philosophers  are  not  to  be  wholly 
despised. 

I  know  that  I  am  advancing  a  great  paradox  in 
pretending  to  resuscitate  in  some  sort  the  ancient 
philosophy^  and  to  recall  postliminio  the  substan- 
tial forms  almost  banished  from  our  modern  thought. 
But  perhaps  I  will  not  be  condemned  lightly  when 
it  is  known  that  I  have  long  meditated  over  the 
modern  philosophy  and  that  I  have  devoted  much 
time  to  experiments  in  physics  and  to  the  demon- 
strations of  geometry  and  that  I,  too,  for  a  long  time 
was  persuaded  of  the  baselessness  of  those  "beings" 
which,  however,  I  was  finally  obliged  to  take  up 
again  in  spite  of  myself  and  as  though  by  force. 


l8  LEIBNIZ. 

The  many  investigations  which  I  carried  on  com- 
pelled me  to  recognize  that  our  moderns  do  not  do 
sufficient  justice  to  Saint  Thomas  and  to  the  other 
great  men  of  that  period  and  that  there  is  in  the 
theories  of  the  scholastic  philosophers  and  theo- 
logians far  more  solidity  than  is  imagined,  provided 
that  these  theories  are  employed  a  propos  and  in 
their  place.  I  am  persuaded  that  if  some  careful 
and  meditative  mind  were  to  take  the  trouble  to 
clarify  and  direct  their  thoughts  in  the  manner  of 
analytic  geometers,  he  would  find  a  great  treasure 
of  very  important  truths,  wholly  demonstrable. 

XII.  That  the  conception  of  the  extension  of  a  body 
is  in  a  way  imaginary  and  does  not  constitute  the  sub- 
stance of  the  body. 

But  to  resume  the  thread  of  our  discussion,  I 
believe  that  he  who  will  meditate  upon  the  nature 
of  substance,  as  I  have  explained  it  above,  will  find 
that  the  whole  nature  of  bodies  is  not  exhausted  in 
their  extension,  that  is  to  say,  in  their  size,  figure 
and  motion,  but  that  we  must  recognize  something 
which  corresponds  to  soul,  something  which  is  com- 
monly called  substantial  form,  although  these  forms 
effect  no  change  in  the  phenomena,  any  more  than 
do  the  souls  of  beasts,  that  is  if  they  have  souls. 
It  is  even  possible  to  demonstrate  that  the  ideas  of 
size,  figure  and  motion  are  not  so  distinctive  as  is 
imagined,  and  that  they  stand  for  something  imag- 
inary relative  to  our  preceptions  as  do,  although  to 
a  greater  extent,  the  ideas  of  color,  heat,  and  the 
other  similar  qualities  in  regard  to  which  we  may 
doubt  whether  they  are  actually  to  be  found  in  the 
nature  of  the  things  outside  of  us.  This  is  why 


DISCOURSE    ON   METAPHYSICS.  19 

these  latter  qualities  are  unable  to  constitute  "sub- 
stance" and  if  there  is  no  other  principle  of  identity 
in  bodies  than  that  which  has  just  been  referred  to 
a  body  would  not  subsist  more  than  for  a  moment. 
The  souls  and  the  substance-forms  of  other  bodies 
are  entirely  different  from  intelligent  souls  which 
alone  know  their  actions,  and  not  only  do  not  perish 
through  natural  means  but  indeed  always  retain  the 
knowledge  of  what  they  are;  a  fact  which  makes 
them  alone  open  to  chastisement  or  recompense, 
and  makes  them  citizens  of  the  republic  of  the  uni- 
verse whose  monarch  is  God.  Hence  it  follows  that 
all  the  other  creatures  should  serve  them,  a  point 
which  we  shall  discuss  more  amply  later. 

XIII.  As  the  individual  concept  of  each  person 
includes  once  for  all  everything  which  can  ever  happen 
to  him,  in  it  can  be  seen,  a  priori  the  evidences  or  the 
reasons  for  the  reality  of  each  event,  and  why  one  hap- 
pened sooner  than  the  other.  But  these  events,  how- 
ever certain,  are  nevertheless  contingent,  being  based 
on  the  free  choice  of  God  and  of  his  creatures.  It  is 
true  that  their  choices  always  have  their  reasons,  but 
they  incline  to  the  choices  under  no  compulsion  of 
necessity. 

But  before  going  further  it  is  necessary  to  meet  a 
difficulty  which  may  arise  regarding  the  principles 
which  we  have  set  forth  in  the  preceding.  We  have 
said  that  the  concept  of  an  individual  substance 
includes  once  for  all  everything  which  can  ever  hap- 
pen to  it  and  that  in  considering  this  concept  one  will 
be  able  to  see  everything  which  can  truly  be  said 
concerning  the  individual,  just  as  we  are  able  to 
see  in  the  nature  of  a  circle  all  the  properties  which 


20  LEIBNIZ. 

can  be  derived  from  it.  But  does  it  not  seem  that 
in  this  way  the  difference  between  contingent  and 
necessary  truths  will  be  destroyed,  that  there  will 
be  no  place  for  human  liberty,  and  that  an  absolute 
fatality  will  rule  as  well  over  all  our  actions  as  over 
all  the  rest  of  the  events  of  the  world?  To  this  I 
reply  that  a. distinction  must  be  made  between  that 
which  is  certain  and  that  which  is  necessary.  Every 
one  grants  that  future  contingencies  are  assured 
since  God  foresees  them,  but  we  do  not  say  just 
because  of  that  that  they  are  necessary.  But  it  will 
be  objected,  that  if  any  conclusion  can  be  deduced 
infallibly  from  some  definition  or  concept,  it  is 
necessary;  and  now  since  we  have  maintained  that 
everything  which  is  to  happen  to  anyone  is  already 
virtually  included  in  his  nature  or  concept,  as  all 
the  properties  are  contained  in  the  definition  of 
a  circle,  therefore,  the  difficulty  still  remains.  In 
order  to  meet  the  objection  completely,  I  say 
that  the  connection  or  sequence  is  of  two  kinds; 
the  one,  absolutely  necessary,  whose  contrary  im- 
plies contradiction,  occurs  in  the  eternal  verities 
like  the  truths  of  geometry;  the  other  is  necessary 
only  ex  hypothesi,  and  so  to  speak  by  accident, 
and  in  itself  it  is  contingent  since  the  contrary  is 
not  implied.  This  latter  sequence  is  not  founded 
upon  ideas  wholly  pure  and  upon  the  pure  under- 
standing of  God,  but  upon  his  free  decrees  and  upon 
the  processes  of  the  universe.  Let  us  give  an 
example.  Since  Julius  Caesar  will  become  perpet- 
ual Dictator  and  master  of  the  Republic  and  will 
overthrow  the  liberty  of  Rome,  this  action  is  con- 
tained in  his  concept,  for  we  have  supposed  that  it 
is  the  nature  of  such  a  perfect  concept  of  a  subject 


DISCOURSE    ON    METAPHYSICS.  21 

to  involve  everything,  in  fact  so  that  the  predicate 
may  be  included  in  the  subject  ut  possit  inesse  sub- 
jecto.  We  may  say  that  it  is  not  in  virtue  of  this 
concept  or  idea  that  he  is  obliged  to  perform  this 
action,  since  it  pertains  to  him  only  because  God 
knows  everything.  But  it  will  be  insisted  in  reply 
that  his  nature  or  form  responds  to  this  concept, 
and  since  God  imposes  upon  him  this  personality, 
he  is  compelled  henceforth  to  live  up  to  it.  I 
could  reply  by  instancing  the  similar  case  of  the 
future  contingencies  which  as  yet  have  no  reality 
save  in  the  understanding  and  will  of  God, and  which, 
because  God  has  given  them  in  advance  this  form, 
must  needs  correspond  to  it.  But  I  prefer  to  over- 
come a  difficulty  rather  than  to  excuse  it  by  instanc- 
ing other  difficulties,  and  what  I  am  about  to  say 
will  serve  to  clear  up  the  one  as  well  as  the  other. 
It  is  here  that  must  be  applied  the  distinction  in 
the  kind  of  relation,  and  I  say  that  that  which  hap- 
pens conformably  to  these  decrees  is  assured,  but 
that  it  is  not  therefore  necessary,  and  if  anyone  did 
the  contrary,  he  would  do  nothing  impossible  in 
itself,  although  it  is  impossible  ex  hypothesi  that  that 
other  happen.  For  if  anyone  were  capable  of  carry- 
ing out  a  complete  demonstration  by  virtue  of  which 
he  could  prove  this  connection  of  the  subject,  which 
is  Caesar,  with  the  predicate, .which  is  his  successful 
enterprise,  he  would  bring  us  to  see  in  fact  that  the 
future  dictatorship  of  Caesar  had  its -basis  in  his 
concept  or  nature,  so  that  one  would  see  there  a 
reason  why  he  resolved  to  cross  the  Rubicon  rather 
than  to  stop,  and  why  he  gained  instead  of  losing 
the  day  at  Pharsalus,  and  that  it  was  reasonable  and 
by  consequence  assured  that  this  would  occur,  but 


22  LEIBNIZ. 

one  would  not  prove  that  it  was  necessary  in  itself, 
nor  that  the  contrary  implied  a  contradiction, 
almost  in  the  same  way  in  which  it  is  reasonable  and 
assured  that  God  will  always  do  what  is  best 
although  that  which  is  le'ss  perfect  is  not  thereby 
implied.  For  it  would  be  found  that  this  demon- 
stration of  this  predicate  as  belonging  to  Caesar  is 
not  as  absolute  as  are  those  of  numbers  or  of  geom- 
etry, but  that  this  predicate  supposes  a  sequence  of 
things  which  God  has  shown  by  his  free  will.  This 
sequence  is  based  on  the  first  free  decree  of  God 
which  was  to  do  always  that  which  is  the  most 
perfect  and  upon  the  decree  which  God  made  fol- 
lowing the  first  one,  regarding  human  nature,  which 
is  that  men  should  always  do,  although  freely,  that 
which  appears  to  be  the  best.  Now  every  truth 
which  is  founded  upon  this  kind  of  decree  is  con- 
tingent, although  certain,  for  the  decrees  of  God  do 
not  change  the  possibilities  of  things  and,  as  1  have 
already  said,  although  God  assuredly  chooses  the 
best,  this  does  not  prevent  that  which  is  less  per- 
fect from  .being  possible  in  itelf.  Although  it  will 
never  happen,  it  is  not  its  impossibility  but  its 
imperfection  which  causes  him  to  reject  it.  Now 
nothing  is  necessitated  whose  opposite  is  possible. 
One  will  then  be  in  a  position  to  satisfy  these  kinds 
of  difficulties,  however  great  they  may  appear  (and 
in  fact  they  have  not  been  less  vexing  to  all  other 
thinkers  who  have  ever  treated  this  matter),  pro- 
vided that  he  considers  well  that  all  contingent 
propositions  have  reasons  why  they  are  thus,  rather 
than  otherwise,  or  indeed  (what  is  the  same  thing) 
that  they  have  proof  a  priori  of  their  truth,  which 
render  them  certain  and  show  that  the  connection 


DISCOURSE   ON    METAPHYSICS.  23 

of  the  subject  and  predicate  in  these  propositions 
has  its  basis  in  the  nature  of  the  one  and  of  the 
other,  but  he  must  further  remember  that  such  con- 
tingent propositions  have  not  the  demonstrations 
of  necessity,  since  their  reasons  are  founded  only  on 
the  principle'  of  contingency  or  of  the  existence  of 
things,  that  is  to  say,  upon  that  which  is,  or  which 
appears  to  be  the  best  among  several  things  equally 
possible.  Necessary  truths,  on  the  other  hand,  are 
founded  upon  the  principle  of  contradiction,  and 
upon  the  possibility  or  impossibility  of  the  essences 
themselves,  without  regard  here  to  the  free  will  of 
God  or  of  creatures. 


XIV.  God  produces  different  substances  according  to 
the  different  views  which  he  has  of  the  world,  and  by 
the  intervention  of  God,  the  appropriate  nature  of  each 
substance  brings  it  about  that  what  happens  to  one 
corresponds  to  what  happens  to  all  the  others,  without, 
however,  their  acting  upon  one  another  directly. 

After  having  seen,  to  a  certain  extent,  in  what  the 
nature  of  substances  consists,  we  must  try  to  explain 
the  dependence  they  have  upon  one  another  and 
their  actions  and  passions.  Now  it  is  first  of  all 
very  evident  that  created  substances  depend  upon 
God  who  preserves  them  and  can  produce  them 
continually  by  a  kind  of  emanation  just  as  we  pro- 
duce our  thoughts,  for  when  God  turns,  so  to  say, 
on  all  sides  and  in  all  fashions,  the  general  system 
of  phenomena  which  he  finds  it  good  to  produce  for 
the  sake  of  manifesting  his  glory,  and  when  he 
regards  all  the  aspects  of  the  world  in  all  possible 
manners,  since  there  is  no  relation  which  escapes 


24  LEIBNIZ. 

his  omniscience,  the  result  of  each  view  of  the  uni- 
verse as  seen  from  a  different  position  is  a  sub- 
stance which  expresses  the  universe  conformably 
to  this  view,  provided  God  sees  fit  to  render  his 
thought  effective  and  to  produce  the  substance, 
and  since  God's  vision  is  always  true,  our  per- 
ceptions are  always  true  and  that  which  deceives 
us  are  our  judgments,  which  are  of  us.  Now  we 
have  said  before,  and  it  follows  from  what  we 
have  just  said  that  each  substance  is  a  world  by 
itself,  independent  of  everything  else  excepting 
God;  therefore,  all  our  phenomena  that  is  all  things 
which  are  ever  able  to  happen  to  us,  are  only  con- 
sequences of  our  being.  Now  as  the  phenomena 
maintain  a  certain  order  conformably  to  our  nature, 
or  so  to  speak  to  the  world  which  is  in  us  (from 
whence  it  follows  that  we  can,  for  the  regulation  of 
our  conduct,  make  useful  observations  which  are 
justified  by  the  outcome  of  the  future  phenomena) 
and  as  we  are  thus  able  often  to  judge  the  future  by 
the  past  without  deceiving  ourselves,  we  have  suffi- 
cient grounds  for  saying  that  these  phenomena  are 
true  and  we  will  not  be  put  to  the  task  of  inquiring 
whether  they  are  outside  of  us,  and  whether  others 
perceive  them  also. 

Nevertheless  it  is  most  true  that  the  perceptions 
and  expressions  of  all  substances  intercorrespond, 
so  that  each  one  following  independently  certain 
reasons  or  laws  which  he  has  noticed  meets  others 
which  are  doing  the  same,  as  when  several  have 
agreed  to  meet  together  in  a  certain  place  on  a  set 
day,  they  are  able  to  carry  out  the  plan  if  they  wish. 
Now  although  all  express  the  same  phenomena, 
this  does  not  bring  it  about  that  their  expressions 


DISCOURSE   ON    METAPHYSICS.  25 

are  exactly  alike.  It  is  sufficient  if  they  are  pro- 
portional. As  when  several  spectators  think  they 
see  the  same  thing  and  are  agreed  about  it,  although 
each  one  sees  or  speaks  according  to  the  measure 
of  his  vision.  It  is  God  alone,  (from  whom  all 
individuals  emanate  continually,  and  who  sees  the 
universe  not  only  as  they  see  it,  but  besides  in  a 
very  different  way  from  them)  who  is  the  cause  of 
this  correspondence  in  their  phenomena  and  who 
brings  it  about  that  that  which  is  particular  to  one, 
is  also  common  to  all,  otherwise  there  would  be  no 
relation.  In  a  way,  then,  we  might  properly  say, 
although  it  seems  strange,  that  a  particular  sub- 
stance never  acts  upon  another  particular  substance 
nor  is  it  acted  upon  by  it.  That  which  happens  to 
each  one  is  only  the  consequence  of  its  complete 
idea  or  concept,  since  this  idea  already  includes  all 
the  predicates  and  expresses  the  whole  universe. 
In  fact  nothing  can  happen  to  us  except  thoughts 
and  perceptions,  and  all  our  thoughts  and  percep- 
tions are  but  the  consequence,  contingent  it  is  true, 
of  our  precedent  thoughts  and  perceptions,  in  such 
a  way  that  were  I  able  to  consider  directly  all  that 
happens  or  appears  to  me  at  the  present  time,  I 
should  be  able  to  see  all  that  will  happen  to  me  or 
that  will  ever  appear  to  me.  This  future  will  not 
fail  me,  and  will  surely  appear  to  me  even  if  all 
that  which  is  outside  of  me  were  destroyed,  save 
only  that  God  and  myself  were  left. 

Since,  however,  we  ordinarily  attribute  to  other 
things  an  action  upon  us  which  brings  us  to  per- 
ceive things  in  a  certain  manner,  it  is  necessary  to 
consider  the  basis  of  this  judgment  and  to  inquire 
what  there  is  of  truth  in  it. 


26  LEIBNIZ. 

XV.  The  action  of  one  finite  substance  upon  another 
consists  only  in  the  increase  in  the  degrees  of  the 
expression  of  the  first  combined  with  a  decrease  in  that 
of  the  second,  in  so  far  as  God  has  in  advance  fashioned 
them  so  that  they  shall  act  in  accord. 

Without  entering  into  a  long  discussion  it  is  suffi- 
cient for  reconciling  the  language  of  metaphysics 
with  that  of  practical  life  to  remark  that  we  pref- 
erably attribute  to  ourselves,  and  with  reason,  the 
phenomena  which  we  express  the  most  perfectly, 
and  that  we  attribute  to  other  substances  those 
phenomena  which  each  one  expresses  the  best. 
Thus  a  substance,  which  is  of  an  infinite  extension 
in  so  far  as  it  expresses  all,  becomes  limited  in  pro- 
portion to  its  more  or  less  perfect  manner  of  expres- 
sion. It  is  thus  then  that  we  may  conceive  of 
substances  as  interfering  with  and  limiting  one 
another,  and  hence  we  are  able  to  say  that  in  this 
sense  they  act  upon  one  another,  and  that  they,  so 
to  speak,  accommodate  themselves  to  one  another. 
For  it  can  happen  that  a  single  change  which  aug- 
ments the  expression  of  the  one  may  diminish  that 
of  the  other.  Now  the  virtue  of  a  particular  sub- 
stance is  to  express  well  the  glory  of  God,  and  the 
better  it  expresses  it,  the  less  is  it  limited.  Every- 
thing when  it  expresses  its  virtue  or  power,  that  is 
to  say,  when  it  acts,  changes  to  better,  and  expands 
just  in  so  far  as  it  acts.  When  therefore  a  change 
occurs  by  which  several  substances  are  affected  (in 
fact  every  change  affects  them  all)  I  think  we  may 
say  that  those  substances,  which  by  this  change 
pass  immediately  to  a  greater  degree  of  perfection, 
or  to  a  more  perfect  expression,  exert  power  and 


DISCOURSE    ON    METAPHYSICS.  27 

act,  while  those  which  pass  to  a  lesser  degree  dis- 
close their  weakness  and  suffer.  I  also  hold  that 
every  activity  of  a  substances  which  has  perception 
implies  some  pleasure,  and  every  passion  some  pain, 
except  that  it  may  very  well  happen  that  a  present 
advantage  will  be  eventually  destroyed  by  a  greater 
evil,  whence  it  comes  that  one  may  sin  in  acting  or 
exerting  his  power  and  in  finding  pleasure. 

XVI.  The  extraordinary  intervention  of  God  is  not 
excluded  in  that  which  our  particular  essences  express, 
because  their  expression  includes  everything.  Such 
intervention,  however,  goes  beyond  the  power  of  our 
natural  being  or  of  our  distinct  expression,  because 
these  are  finite,  and  follow  certain  subordinate  regula- 
tions. 

There  remains  for  us  at  present- only  to  explain 
how  it  is  possible  that  God  has  influence  at  times 
upon  men  or  upon  other  substances  by  an  extraor- 
dinary or  miraculous  intervention,  since  it  seems 
that  nothing  is  able  to  happen  which  is  extraor- 
dinary or  supernatural  in  as  much  as  all  the  events 
which  occur  to  the  other  substances  are  only  the 
consequences  of  their  natures.  We  must  recall 
what  was  said  above  in  regard  to  the  miracles  in 
the  universe.  These  always  conform  to  the  univer- 
sal law  of  the  general  order,  although  they  may  con- 
travene the  subordinate  regulations,  and  since  every 
person  or  substance  is  like  a  little  world  which 
expresses  the  great  world,  we  can  say  that  this 
extraordinary  action  of  God  upon  this  substance 
is  nevertheless  miraculous,  although  it  is  comprised 
in  the  general  order  of  the  universe  in  so  far  as  it 


28  LEIBNIZ. 

is  expressed  by  the  individual  essence  or  concept 
of  this  substance.  This  is  why,  if  we  understand 
in  our  natures  all  that  they  express,  nothing  is  sup- 
ernatural in  them,  because  they  reach  out  to  every- 
thing, an  effect  always  expressing  its  cause,  and 
God  being  the  veritable  cause  of  the  substances. 
But  as  that  which  our  natures  express  the  most  per- 
fectly pertains  to  them  in  a  particular  manner,  that 
being  their  special  power,  and  since  they  are  limited, 
as  I  have  just  explained,  many  things  there  are 
which  surpass  the  powers  of  our  natures  and  even 
of  all  limited  natures  As  a  consequence,  to  speak 
more  clearly,  I  say  that  the  miracles  and  the  extraor- 
dinary interventions  of  God  have  this  peculiarity 
that  they  cannot  be  foreseen  by  any  created  mind 
however  enlightened.  This  is  because  the  distinct 
comprehension  of  the  fundamental  order  surpasses 
them  all,  while  on  the  other  hand,  that  which  is 
called  natural  depends  upon  less  fundamental  reg- 
ulations which  the  creatures  are  able  to  understand. 
In  order  then  that  my  words  may  be  as  irreprehen- 
sible  as  the  meaning  I  am  trying  to  convey,  it  will 
be  well  to  associate  certain  words  with  certain  sig- 
nifications. We  may  call  that  which  includes  every- 
thing that  we  express  and  which  expresses  our 
union  with  God  himself,  nothing  going  beyond  it, 
our  essence.  But  that  which  is  limited  in  us  may  be 
designated  as  our  nature  or  our  power  and  in  accor- 
dance with  this  terminology  that  which  goes 
beyond  the  natures  of  all  created  substances  is 
supernatural. 


DISCOURSE   ON    METAPHYSICS.  29 

XVII.  An  example  of  a  subordinate  regulation  in 
the  law  of  nature  which  demonstrates  that  God  always 
preserves  the  same  amount  of  force  but  not  the  same 
quantity  of  motion : — against  the  Cartesians  and  many 
others. 

I  have  frequently  spoken  of  subordinate  regula- 
tions, or  of  the  laws  of  nature,  and  it  seems  that 
it  will  be  well  to  give  an  example.  Our  new 
philosophers  are  unanimous  in  employing  that 
famous  law  that  God  always  preserves  the  same 
amount  of  motion  in  the  universe.  In  fact  it  is  a 
very  plausible  law,  and  in  times  past  I  held  it  for 
indubitable.  But  since  then  I  have  learned  in  what 
its  fault  consists.  Monsieur  Descartes  and  many 
other  clever  mathematicians  have  thought  that  the 
quantity  of  motion,  that  is  to  say  the  velocity  mul- 
tiplied by  the  mass*  of  the  moving  body,  is  exactly 
equivalent  to  the  moving  force,  or  to  speak  in 
mathematical  terms  that  the  force  varies  as  the 
velocity  multiplied  by  the  mass.  Now  it  is  rea- 
sonable that  the  same  force  is  always  preserved  in 
the  universe.  So  also,  looking  to  phenomena,  it 
will  be  readily  seen  that  a  mechanical  perpetual 
motion  is  impossible,  because  the  force  in  such  a 
machine,  being  always  diminished  a  little  by  fric- 

*This  term  is  employed  here  for  the  sake  of  clearness. 
Leibniz  did  not  possess  the  concept  "mass,"  which  was 
enunciated  by  Newton  in  the  same  year  in  which  the  present 
treatise  was  written,  1686.  Leibniz  uses  the  terms  "body," 
"magnitude  of  body, "  etc.  The  technical  expression  "mass" 
occurs  once  only  in  the  writings  of  Leibniz  (in  a  treatise  pub- 
lished in  1695),  and  was  there  doubtless  borrowed  from  Newton. 
For  the  history  of  the  controversy  concerning  the  Cartesian  and 
Leibnizian  measure  of  force,  see  Mach's  Science  of  Mechanics, 
Chicago,  1893,  pp.  272  et  seq. — Trans. 


30  LEIBNIZ. 

tion  and  so  ultimately  destined  to  be  entirely  spent, 
would  necessarily  have  to  recoup  its  losses,  and  con- 
sequently would  keep  on  increasing  of  itself  without 
any  new  impulsion  from  without;  and  we  see  further- 
more that  the  force  of  a  body  is  diminished  only 
in  proportion  as  it  gives  up  force,  either  to  a  con- 
tiguous body  or  to  its  own  parts,  in  so  far  as  they 
have  a  separate  movement.  The  mathematicians  to 
whom  I  have  referred  think  that  what  can  be  said  of 
force  can  be  said  of  the  quantity  of  motion.  In 
order,  however,  to  show  the  difference  I  make  two 
suppositions:  in  the  first  place,  that  a  body  falling 
from  a  certain  height  acquires  a  force  enabling  it  to 
remount  to  the  same  height,  provided  that  its  direc- 
tion is  turned  that  way,  or  provided  that  there  are 
no  hindrances.  For  instance,  a  pendulum  will  rise 
exactly  to  the  height  from  which  it  has  fallen,  pro- 
vided the  resistance  of  the  air  and  of  certain  other 

small  particles  do  not  di- 
minish a  little  its  acquired 
force. 

I  suppose  in  the  second 
place  that  it  will  take  as 
much  force  to  lift  a  body 
A  weighing  one  pound 
to  the  height  CD,  four 
feet,  as  to  raise  a  body  B 
weighing  four  pounds  to 
the  height  EF,  one  foot. 
These  two  suppositions  are  granted  by  our  new 
philosophers.  It  is  therefore  manifest  that  the 
body  A  falling  from  the  height  CD  acquires  exactly 
as  much  force  as  the  body  B  falling  from  the  height 
EF,  for  the  body  B  at  F,  having  by  the  first  suppo- 


(f\ 
(  } 


DISCOURSE    ON    METAPHYSICS.  31 

sition  sufficient  force  to  return  to  E,  has  therefore 
the  force  to  carry  a  body  of  four  pounds  to  the  dis- 
tance of  one  foot,  EF.  And  likewise  the  body 
A  at  D,  having  the  force  to  return  to  C,  has  also 
the  force  required  to  carry  a  body  weighing  one 
pound,  its  own  weight,  back  to  C,  a  distance  of  four 
feet.  Now  by  the  second  supposition  the  force 
of  these  two  bodies  is  equal.  Let  us  now  see  if  the 
quantity  of  motion  is  the  same  in  each  case.  It  is 
here  that  we  will  be  surprised  to  find  a  very  great 
difference,  for  it  has  been  proved  by  Galileo  that 
the  velocity  acquired  by  the  fall  CD  is  double  the 
velocity  acquired  by  the  fall  EF,  although  the 
height  is  four  times  as  great.  Multiplying,  there- 
fore, the  body  A,  whose  mass  is  I,  by  its  velocity, 
which  is  2,  the  product  or  the  quantity  of  move- 
ment will  be  2,  and  on  the  other  hand,  if  we  multi- 
ply the  body  B,  whose  mass  is  4,  by  its  velocity, 
which  is  i,  the  product  or  quantity  of  motion  will 
be  4.  Hence  the  quantity  of  the  motion  of  the 
body  A  at  the  point  D  is  half  the  quantity  of  motion 
of  the  body  B  at  the  point  F,  yet  their  forces  are 
equal,  and  there  is  therefore  a  great  difference 
between  the  quantity  of  motion  and  the  force.  This 
is  what  we  set  out  to  show.  We  can  see  therefore 
how  the  force  ought  to  be  estimated  by  the  quantity 
of  the  effect  which  it  is  able  to  produce,  for  exam- 
ple by  the  height  to  which  a  body  of  certain  weight 
can  be  raised.  This  is  a  very  different  thing  from 
the  velocity  which  can  be  imparted  to  it,  and  in 
order  to  impart  to  it  double  the  velocity  we  must 
have  double  the  force.  Nothing  is  simpler  than 
this  proof  and  Monsieur  Descartes  has  fallen  into 
error  here,  only  because  he  trusted  too  much  to  his 


32  LEIBNIZ. 

thoughts  even  when  they  had  not  been  ripened  by 
reflection.  But  it  astonishes  me  that  his  disciples 
have  not  noticed  this  error,  and  I  am  afraid  that 
they  are  beginning  to  imitate  little  by  little  certain 
Peripatetics  whom  they  ridicule,  and  that  they  are 
accustoming  themselves  to  consult  rather  the  books 
of  their  master,  than  reason  or  nature. 

XVIII.  The  distinction  between  force  and  the  quan- 
tity of  motion  is,  among  other  reasons,  important  as 
showing  that  we  must  have  recourse  to  metaphysical 
considerations  in  addition  to  discussions  of  extension  if 
we  wish  to  explain  the  phenomena  of  matter. 

This  consideration  of  the  force,  distinguished 
from  the  quantity  of  motion  is  of  importance,  not 
only  in  physics  and  mechanics  for  rinding  the  real 
laws  of  nature  and  the  principles  of  motion,  and 
even  for  correcting  many  practical  errors  which 
have  crept  into  the  writings  of  certain  able  mathe- 
maticians, but  also  in  metaphysics  it  is  of  impor- 
tance for  the  better  understanding  of  principles. 
Because  motion,  if  we  regard  only  its  exact  and 
formal  meaning,  that  is,  change  of  place,  is  not 
something  entirely  real,  and  when  several  bodies 
change  their  places  reciprocally,  it  is  not  possible 
to  determine  by  considering  the  bodies  alone  to 
which  among  them  movement  or  repose  is  to  be 
attributed,  as  I  could  demonstrate  geometrically, 
if  I  wished  to  stop  for  it  now.  But  the  force,  or 
the  proximate  cause  of  these  changes  is  something 
more  real,  and  there  are  sufficient  grounds  for 
attributing  it  to  one  body  rather  than  to  another,  and 
it  is  only  through  this  latter  investigation  that  we 
can  determine  to  which  one  the  movement  must 


DISCOURSE    ON    METAPHYSICS.  33 

appertain.  Now  this  force  is  something  different 
from  size,  from  form  or  from  motion,  and  it  can  be 
seen  from  this  consideration  that  the  whole  mean- 
ing of  a  body  is  not  exhausted  in  its  extension 
together  with  its  modifications  as  our  moderns  per- 
suade themselves.  We  are  therefore  obliged  to 
restore  certain  beings  or  forms  which  they  have  ban- 
ished. It  appears  more  and  more  clear  that  although 
all  the  particular  phenomena  of  nature  can  be 
explained  mathematically  or  mechanically  by  those 
who  understand  them,  yet  nevertheless,  the  general 
principles  of  corporeal  nature  and  even  of  mechan- 
ics are  metaphysical  rather  than  geometric,  and 
belong  rather  to  certain  indivisible  forms  or  natures 
as  the  causes  of  the  appearances,  than  to  the  cor- 
poreal mass  or  to  extension.  This  reflection  is 
able  to  reconcile  the  mechanical  philosophy  of  the 
moderns  with  the  circumspection  of  those  intelli- 
gent and  well-meaning  persons  who,  with  a  certain 
justice,  fear  that  we  are  becoming  too  far  removed 
from  immaterial  beings  and  that  we  are  thus  preju- 
dicing piety. 

XIX.  The  utility  of  final  causes  in  Physics. 

As  I  do  not  wish  to  judge  people  in  ill  part  I 
bring  no  accusation  against  our  new  philosophers 
who  pretend  to  banish  final  causes  from  physics,  but 
I  am  nevertheless  obliged  to  avow  that  the  conse- 
quences of  such  a  banishment  appear  to  me  danger- 
ous, especially  when  joined  to  that  position  which 
I  refuted  at  the  beginning  of  this  treatise.  That 
position  seemed  to  go  the  length  of  discarding  final 
causes  entirely  as  though  God  proposed  no  end  and 
no  good  in  his  activity,  or  as  if  good  were  not  to  be 


34  LEIBNIZ. 

the  object  of  his  will.  I  hold  on  the  contrary  that 
it  is  just  in  this  that  the  principle  of  all  existences 
and  of  the  laws  of  nature  must  be  sought,  hence 
God  always  proposes  the  best  and  most  perfect.  I 
am  quite  willing  to  grant  that  we  are  liable  to  err 
when  we  wish  to  determine  the  purposes  or  councils 
of  God,  but  this  is  the  case  only  when  we  try  to 
limit  them  to  some  particular  design,  thinking  that 
he  has  had  in  view  only  a  single  thing,  while  in 
fact  he  regards  everything  at  once.  As  for  instance, 
if  we  think  that  God  has  made  the  world  only  for 
us,  it  is  a  great  blunder,  although  it  may  be  quite 
true  that  he  has  made  it  entirely  for  us,  and  that 
there  is  nothing  in  the  universe  which  does  not 
touch  us  and  which  does  not  accommodate  itself  to 
the  regard  which  he  has  for  us  according  to  the 
principle  laid  down  above.  Therefore  when  we 
see  some  good  effect  or  some  perfection  which  hap- 
pens or  which  follows  from  the  works  of  God  we  are 
able  to  say  assuredly  that  God  has  purposed  it,  for 
he  does  nothing  by  chance,  and  is  not  like  us  who 
sometimes  fail  to  do  well.  Therefore,  far  from 
being  able  to  fall  into  error  in  this  respect  as  do  the 
extreme  statesmen  who  postulate  too  much  foresight 
in  the  designs  of  Princes,  or  as  do  commentators 
who  seek  for  too  much  erudition  in  their  authors,  it 
will  be  impossible  to  attribute  too  much  reflection 
to  God's  infinite  wisdom,  and  there  is  no  matter  in 
which  error  is  less  to  be  feared  provided  we  confine 
ourselves  to  affirmations  and  provided  we  avoid 
negative  statements  which  limit  the  designs  of  God. 
All  those  who  see  the  admirable  structure  of  ani- 
mals find  themselves  led  to  recognize  the  wisdom 
of  the  author  of  things  and  I  advise  those  who  have 


DISCOURSE    ON    METAPHYSICS.  35 

any  sentiment  of  piety  and  indeed  of  true  philos- 
ophy to  hold  aloof  from  the  expressions  of  certain 
pretentious  minds  who  instead  of  saying  that  eyes 
were  made  for  seeing,  say  that  we  see  because  we 
find  ourselves  having  eyes.  When  one  seriously 
holds  such  opinions  which  hand  everything  over  to 
material  necessity  or  to  a  kind  of  chance  (although 
either  alternative  ought  to  appear  ridiculous  to 
those  who  understand  what  we  have  explained 
above)  it  is  difficult  to  recognize  an  intelligent 
author  of  nature.  The  effect  should  correspond  to 
its  cause  and  indeed  it  is  best  known  through  the 
recognition  of  its  cause,  so  that  it  is  reasonable  to 
introduce  a  sovereign  intelligence  ordering  things, 
and  in  place  of  making  use  of  the  wisdom  of  this  sov- 
ereign being,  to  employ  only  the  properties  of  matter 
to  explain  phenomena.  As  'if  in  order  to  account 
for  the  capture  of  an  important  place  by  a  prince, 
the  historian  should  say  it  was  because  the  particles 
of  powder  in  the  cannon  having  been  touched  by  a 
spark  of  fire  expanded  with  a  rapidity  capable  of 
pushing  a  hard  solid  body  against  the  walls  of  the 
place,  while  the  little  particles  which  composed  the 
brass  of  the  cannon  were  so  well  interlaced  that 
they  did  not  separate  under  this  impact, — as  if  he 
should  account  for  it  in  this  way  instead  of  making 
us  see  how  the  foresight  of  the  conqueror  brought 
him  to  choose  the  time  and  the  proper  means  and 
how  his  ability  surmounted  all  obstacles. 

XX.  A  noteworthy  disquisition  in  Plato's  Phaedo 
against  the  philosophers  who  were  too  materialistic. 

This  reminds  me  of  a  fine  disquisition  by  Socrates 
in  Plato's  Phaedo,  which  agrees  perfectly  with  my 


36  LEIBNIZ. 

opinion  on  this  subject  and  seems  to  have  been 
uttered  expressly  for  our  too  materialistic  philos- 
ophers. This  agreement  has  led  me  to  a  desire  to 
translate  it  although  it  is  a  little  long.  Perhaps 
this  example  will  give  some  of  us  an  incentive  to 
share  in  many  of  the  other  beautiful  and  well  bal- 
anced thoughts  which  are  found  in  the  writings  of 
this  famous  author.* 

XXI,  If  the  mechanical  laws  depended  upon  Geome- 
try alone  without  metaphysical  influences,  the  phenom- 
ena would  be  very  different  from  what  they  are. 

Now  since  the  wisdom  of  God  has  always  been 
recognized  in  the  detail  of  the  mechanical  struc- 
tures of  certain  particular  bodies,  it  should  also  be 
shown  in  the  general  economy  of  the  world  and  in 
the  constitution  of  the  laws  of  nature.  This  is  so 
true  that  even  in  the  laws  of  motion  in  general,  the 
plans  of  this  wisdom  have  been  noticed.  For  if 
bodies  were  only  extended  masses,  and  motion  were 
only  a  change  of  place,  and  if  everything  ought  to 
be  and  could  be  deduced  by  geometric  necessity 
from  these  two  definitions  alone,  it  would  follow,  as 
I  have  shown  elsewhere,  that  the  smallest  body  on 
contact  with  a  very  large  one  at  rest  would  impart 
to  it  its  own  velocity,  yet  without  losing  any  of  the 
velocity  that  it  had.  A  quantity  of  other  rules 
wholly  contrary  to  the  formation  of  a  system  would 
also  have  to  be  admitted.  But  the  decree  of  the 
divine  wisdom  in  preserving  always  the  same  force 
and  the  same  total  direction  has  provided  for  a 

*  There  is  a  gap  here  in  the  MS.,  intended  for  the  passage 
from  Plato,  the  translation  of  which  Leibniz  did  not  supply. — 
Trans. 


DISCOURSE    ON    METAPHYSICS.  37 

system.  I  find  indeed  that  many  of  the  effects  of 
nature  can  be  accounted  for  in  a  twofold  way,  that 
is  to  say  by  a  consideration  of  efficient  causes,  and 
again  independently  by  a  consideration  of  final 
causes.  An  example  of  the  latter  is  God's  decree 
to  always  carry  out  his  plan  by  the  easiest  and  most 
determined  way.  I  have  shown  this  elsewhere  in 
accounting  for  the  catoptric  and  dioptric  laws,  and 
I  will  speak  more  at  length  about  it  in  what  follows. 

XXII.  Reconciliation  of  the  two  methods  of  explana- 
tion, the  one  using  final  causes,  and  the  other  efficient 
causes,  thus  satisfying  both  those  who  explain  nature 
mechanically  and  those  who  have  recourse  to  incorpo- 
real natures. 

It  is  worth  while  to  make  the  preceding  remark 
in  order  to  reconcile  those  who  hope  to  explain 
mechanically  the  formation  of  the  first  tissue  of  an 
animal  and  all  the  interrelation  of  the  parts,  with 
those  who  account  for  the  same  structure  by  refer- 
ring to  final  causes.  Both  explanations  are  good; 
both  are  useful  not  only  for  the  admiring  of  the 
work  of  a  great  artificer,  but  also  for  the  discovery  of 
useful  facts  in  physics  and  medicine.  And  writers 
who  take  these  diverse  routes  should  not  speak  ill 
of  each  other.  For  I  see  that  those  who  attempt  to 
explain  beauty  by  the  divine  anatomy  ridicule  those 
who  .imagine  that  the  apparently  fortuitous  flow  of 
certain  liquids  has  been  able  to  produce  such  a 
beautiful  variety  and  that  they  regard  them  as  over- 
bold and  irreverent.  These  others  on  the  contrary 
treat  the  former  as  simple  and  superstitious,  and 
compare  them  to  those  ancients  who  regarded  the 
physicists  as  impious  when  they  maintained  that 


38  LEIBNIZ. 

not  Jupiter  thundered  but  some  material  which  is 
found  in  the  clouds.  The  best  plan  would  be  to 
join  the  two  ways  of  thinking.  To  use  a  practical 
comparison,  we  recognize  and  praise  the  ability  of 
a  workman  not  only  when  we  show  what  designs  he 
had  in  making  the  parts  of  his  machine,  but  also 
when  we  explain  the  instruments  which  he  employed 
in  making  each  part,  above  all  if  these  instruments 
are  simple  and  ingeniously  contrived.  God  is  also 
a  workman  able  enough  to  produce  a  machine  still 
a  thousand  times  more  ingenious  than  is  our  body, 
by  employing  only  certain  quite  simple  liquids  pur- 
posely composed  in  such  a  way  that  ordinary  laws 
of  nature  alone  are  required  to  develop  them  so  as 
to  produce  such  a  marvellous  effect.  But  it  is  also 
true  that  this  development  would  not  take  place  if 
God  were  not  the  author  of  nature.  Yet  I  find  that 
the  method  of  efficient  causes,  which  goes  much 
deeper  and  is  in  a  measure  more  immediate  and  a 
priori,  is  also  more  difficult  when  we  come  to  details, 
and  I  think  that  our  philosophers  are  still  very 
frequently  far  removed  from  making  the  most  of 
this  method.  The  method  of  final  causes,  however, 
is  easier  and  can  be  frequently  employed  to  find  out 
important  and  useful  truths  which  we  should  have 
to  seek  for  a  long  time,  if  we  were  confined  to  that 
other  more  physical  method  of  which  anatomy  is 
able  to  furnish  many  examples.  It  seems  to  me 
that  Snellius,  who  was  the  first  discoverer  of  the  laws 
of  refraction  would  have  waited  a  long  time  before 
finding  them  if  he  had  wished  to  seek  out  first  how 
light  was  formed.  But  he  apparently  followed  that 
method  which  the  ancients  employed  for  Catoptrics, 
that  is,  the  method  of  final  causes.  Because,  while 


DISCOURSE    ON    METAPHYSICS.  39 

seeking  for  the  easiest  way  in  which  to  conduct  a 
ray  of  light  from  one  given  point  to  another  given 
point  by  reflection  from  a  given  plane  (supposing 
that  that  was  the  design  of  nature)  they  discovered 
the  equality  of  the  angles  of  incidence  and  reflec- 
tion, as  can  be  seen  from  a  little  treatise  by  Helio- 
dorus  of  Larissa  and  also  elsewhere.  This  principle 
Mons.  Snellius,  I  believe,  and  afterwards  independ- 
ently of  him,  M.  Fermat,  applied  most  ingeniously 
to  refraction.  For  since  the  rays  while  in  the  same 
media  always  maintain  the  same  proportion  of  sines, 
which  in  turn  corresponds  to  the  resistance  of  the 
media,  it  appears  that  they  follow  the  easiest  way, 
or  at  least  that  way  which  is  the  most  determinate 
for  passing  from  a  given  point  in  one  medium  to  a 
given  point  in  another  medium.  That  demonstra- 
tion of  this  same  theorem  which  M.  Descartes  has 
given,  using  efficient  causes,  is  much  less  satisfac- 
tory. At  least  we  have  grounds  to  think  that  he 
would  never  have  found  the  principle  by  that  means 
if  he  had  not  learned  in  Holland  of  the  discovery 
of  Snellius. 

XXIII.  Returning  to  immaterial  substances  we  ex- 
plain how  God  acts  upon  the  understanding  of  spirits 
and  ask  whether  one  always  keeps  the  idea  of  what  he 
thinks  about. 

I  have  thought  it  well  to  insist  a  little  upon  final 
causes,  upon  incorporeal  natures  and  upon  an 
intelligent  cause  with  respect  to  bodies  so  as  to 
show  the  use  of  these  conceptions  in  physics  and  in 
mathematics.  This  for  two  reasons,  first  to  purge 
from  mechanical  philosophy  the  impiety  that  is 
imputed  to  it,  second,  to  elevate  to  nobler  lines  of 


40  LEIBNIZ. 

thought  the  thinking  of  our  philosophers  who 
incline  to  materialistic  considerations  alone.  Now, 
however,  it  will  be  well  to  return  from  corporeal 
substances  to  the  consideration  of  immaterial 
natures  and  particularly  of  spirits,  and  to  speak  of 
the  methods  which  God  uses  to  enlighten  them  and 
to  act  upon  them.  Although  we  must  not  forget 
that  there  are  here  at  the  same  time  certain  laws  of 
nature  in  regard  to  which  I  can  speak  more  amply 
elsewhere.  It  will  be  enough  for  now  to  touch 
upon  ideas  and  to  inquire  if  we  see  everything  in 
God  and  how  God  is  our  light.  First  of  all  it  will 
be  in  place  to  remark  that  the  wrong  use  of  ideas 
occasions  many  errors.  For  when  one  reasons  in 
regard  to  anything,  he  imagines  that  he  has  an  idea 
of  it  and  this  is  the  foundation  upon  which  certain 
philosophers,  ancient  and  modern,  have  constructed 
a  demonstration  of  God  that  is  extremely  imperfect. 
It  must  be,  they  say,  that  I  have  an  idea  of  God,  or 
of  a  perfect  being,  since  I  think  of  him  and  we  can- 
not think  without  having  ideas;  now  the  idea  of 
this  being  includes  all  perfections  and  since  exist- 
ence is  one  of  these  perfections,  it  follows  that  he 
exists.  But  I  reply,  inasmuch  as  we  often  think 
of  impossible  chimeras,  for  example  of  the  highest 
degree  of  swiftness,  of  the  greatest  number,  of  the 
meeting  of  the  conchoid  with  its  base  or  determinant, 
such  reasoning  is  not  sufficient.  It  is  therefore  in 
this  sense  that  we  can  say  that  there  are  true  and 
false  ideas  according  as  the  thing  which  is  in  ques- 
tion is  possible  or  not.  And  it  is  when  he  is  assured 
of  the  possibility  of  a  thing,  that  one  can  boast  of 
having  an  idea  of  it.  Therefore,  the  aforesaid  argu- 
ment proves  that  God  exists,  if  he  is  possible.  This 


DISCOURSE    ON    METAPHYSICS.  41 

is  in  fact  an  excellent  privilege  of  the  divine  nature, 
to  have  need  only  of  a  possibility  or  an  essence  in 
order  to  actually  exist,  and  it  is  just  this  which  is 
called  ens  a  se. 

XXIV.  What  clear  and  obscure,  distinct  and  con- 
fused, adequate  and  inadequate,  intuitive  and  assumed 
knowledge  is,  and  the  definition  of  nominal,  real,  causal 
and  essential. 

In  order  to  understand  better  the  nature  of  ideas  it 
is  necessary  to  touch  somewhat  upon  the  various 
kinds  of  knowledge.  When  I  am  able  to  recognize  a 
thing  among  others,  without  being  able  to  say  in  what 
its  differences  or  characteristics  consist,  the  knowl- 
edge is  confused.  Sometimes  indeed  we  may  know 
clearly,  that  is  without  being  in  the  slightest  doubt, 
that  a  poem  or  a  picture  is  well  or  badly  done 
because  there  is  in  it  an  "I  know  not  what"  which 
satisfies  or  shocks  us.  Such  knowledge  is  not  yet 
distinct.  It  is  when  I  am  able  to  explain  the  pecu- 
liarities which  a  thing  has,  that  the  knowledge  is 
called  distinct.  Such  is  the  knowledge  of  an 
assayer  who  discerns  the  true  gold  from  the  false  by 
means  of  certain  proofs  or  marks  which  make  up 
the  definition  of  gold.  But  distinct  knowledge  has 
degrees,  because  ordinarily  the  conceptions  which 
enter  into  the  definitions  will  themselves  have  need 
of  definition,  and  are  only  known  confusedly. 
When  at  length  everything  which  enters  into  a 
definition  or  into  distinct  knowledge  is  known  dis- 
tinctly, even  back  to  the  primitive  conception,  I 
call  that  knowledge  adequate.  When  my  mind 
understands  at  once  and  distinctly  all  the  primitive 
ingredients  of  a  conception,  then  we  have  intuitive 


42  LEIBNIZ. 

knowledge.  This  is  extremely  rare  as  most  human 
knowledge  is  only  confused  or  indeed  assumed.  It 
is  well  also  to  distinguish  nominal  from  real  defini- 
tion. I  call  a  definition  nominal  when  there  is 
doubt  whether  an  exact  conception  of  it  is  pos- 
sible; as  for  instance,  when  I  say  that  an  endless 
screw  is  a  line  in  three  dimensional  space  whose 
parts  are  congruent  or  fall  one  upon  another. 
Now  although  this  is  one  of  the  reciprocal  proper- 
ties of  an  endless-  screw,  he  who  did  not  know  from 
elsewhere  what  an  endless  screw  was  could  doubt  if 
such  a  line  were  possible,  because  the  other  lines 
whose  ends  are  congruent  (there  are  only  two:  the 
circumference  of  a  circle  and  the  straight  line)  are 
plane  figures,  that  is  to  say  they  can  be  described 
in  piano.  This  instancfe  enables  us  to  see  that  any 
reciprocal  property  can  serve  as  a  nominal  defini- 
tion, but  when  the  property  brings  us  to  see  the 
possibility  of  a  thing  it  makes  the  definition  real, 
and  as  long  as  one  has  only  a  nominal  definition  he 
cannot  be  sure  of  the  consequences  which  he  draws, 
because  if  it  conceals  a  contradiction  or  an  impos- 
sibility he  would  be  able  to  draw  the  opposite  con- 
clusions. That  is  why  truths  do  not  depend  upon 
names  and  are  not  arbitrary,  as  some  of  our  new 
philosophers  think.  There  is  also  a  considerable 
difference  among  real  definitions,  for  when  the  pos- 
sibility proves  itself  only  by  experience,  as  in  the 
definition  of  quicksilver,  whose  possibility  we  know 
because  such  a  body,  which  is  both  an  extremely 
heavy  fluid  and  quite  volatile,  actually  exists,  the 
definition  is  merely  real  and  nothing  more.  If, 
however,  the  proof  of  the  possibility  is  a  priori,  the 
definition  is  not  cmly  real  but  also  causal  as  for 


DISCOURSE    ON    METAPHYSICS.  43 

instance  when  it  contains  the  possible  generation  of 
a  thing.  Finally  when  the  definition,  without 
assuming  anything  which  requires  a  proof  a  priori 
of  its  possibility,  carries  the  analysis  clear  to  the 
primitive  conception,  the  definition  is  perfect  or 
essential. 

XXV.  In  what  cases  knowledge  is  added  to  mere  con- 
templation of  the  idea. 

Now  it  is  manifest  that  we  have  no  idea  of  a  con- 
ception when  it  is  impossible.  And  in  case  the  knowl- 
edge, where  we  have  the  idea  of  it,  is  only  assumed, 
we  do  not  visualize  it  because  such  a  conception  is 
known  only  in  like  manner  as  conceptions  internally 
impossible.  And  if  it  be  in  fact  possible,  it  is  not 
by  this  kind  of  knowledge  that  we  learn  its  possi- 
bility. For  instance,  when  I  am  thinking  of  a 
thousand  or  of  a  chiliagpn,  I  frequently  do  it  with- 
out contemplating  the  idea.  Even  if  I  say  a  thou- 
sand is  ten  times  a  hundred,  I  frequently  do  not 
trouble  to  think  what  ten  and  a  hundred  are, 
because  I  assume  that  I  know,  and  I  do  not  con- 
sider it  necessary  to  stop  just  at  present  to  conceive 
of  them.  Therefore  it  may  well  happen,  as  it  in 
fact  does  happen  often  enough,  that  I  am  mistaken 
in  regard  to  a  conception  which  I  assume  that  I 
understand,  although  it  is  an  impossible  truth  or  at 
least  is  incompatible  with  others  with  which  I  join 
it,  and  whether  I  am  mistaken  or  not,  this  way  of 
assuming  our  knowledge  remains  the  same.  It  is, 
then,  only  when  our  knowledge  is  clear  in  regard  to 
confused  conceptions,  and  when  it  is  intuitive  in 
regard  to  those  which  are  distinct,  that  we  see  its 
entire  idea. 


44  LEIBNIZ. 

XXVI.  Ideas  are  all  stored  up  within  us.  Plato's 
doctrine  of  reminiscence. 

In  order  to  see  clearly  what  an  idea  is,  we  must 
guard  ourselves  against  a  misunderstanding.  Many 
regard  the  idea  as  the  form  or  the  differentiation  of 
our  thinking,  and  according  to  this  opinion  we  have 
the  idea  in  our  mind,  in  so  far  as  we  are  thinking 
of  it,  and  each  separate  time  that  we  think  of  it 
anew  we  have  another  idea  although  similar  to  the 
preceding  one.  Some,  however,  take  the  idea  as 
the  immediate  object  of  thought,  or  as  a  permanent 
form  which  remains  even  when  we  are  no  longer 
contemplating  it.  As  a  matter  of  fact  our  soul  has 
the  power  of  representing  to  itself  any  form  or 
nature  whenever  the  occasion  comes  for  thinking 
about  it,  and  I  think  that  this  activity  of  bur  soul 
is,  so  far  as  it  expresses  some  nature,  form  or 
essence,  properly  the  idea  of  the  thing.  This  is  in 
us,  and  is  always  in  us,  whether  we  are  thinking  of 
it  or  no.  (Our  soul  expresses  God  and  the  uni- 
verse and  all  essences  as  well  as  all  existences.) 
This  position  is  in  accord  with  my  principles  that 
naturally  nothing  enters  into  our  minds  from  outside. 

It  is  a  bad  habit  we  have  of  thinking  as  though 
our  minds  receive  certain  messengers,  as  it  were,  or 
as  if  they  had  doors  or  windows.  We  have  in  our 
minds  all  those  forms  for  all  periods  of  time 
because  the  mind  at  every  moment  expresses  all  its 
future  thoughts  and  already  thinks  confusedly  of 
all  that  of  which  it  will  ever  think  distinctly. 
Nothing  can  be  taught  us  of  which  we  have  not 
already  in  our  minds  the  idea.  This  idea  is  as  it 
were  the  material  out  of  which  the  thought  will  form 
itself.  This  is  what  Plato  has  excellently  brought 


DISCOURSE    ON    METAPHYSICS.  45 

out  in  his  doctrine  of  reminiscence,  a  doctrine 
which  contains  a  great  deal  of  truth,  provided  that 
it  is  properly  understood  and  purged  of  the  error  of 
pre-existence,  and  provided  that  one  does  not  con- 
ceive of  the  soul  as  having  already  known  and 
thought  at  some  other  time  what  it  learns  and 
thinks  now.  Plato  has  also  confirmed  his  position 
by  a  beautiful  experiment.  He  introduces  a  small 
boy,  whom  he  leads  by  short  steps,  to  extremely 
difficult  truths  of  geometry  bearing  on  incommen- 
surables,  all  this  without  teaching  the  boy  anything, 
merely  drawing  out  replies  by  a  well  arranged  se- 
ries of  questions.  This  shows  that  the  soul  virtually 
knows  those  things,  and  needs  only  to  be  reminded 
(animadverted)  to  recognize  the  truths.  Conse- 
quently it  possesses  at  least  the  idea  upon  which 
those  truths  depend.  We  may  say  even  that  it 
already  possesses  those  truths,  if  we  consider  them 
as  the  relations  of  the  ideas. 

XXVII.  In  what  respect  our  souls  can  be  compared 
to  blank  tablets  and  how  conceptions  are  derived  from 
the  senses. 

Aristotle  preferred  to  compare  our  souls  to  blank 
tablets  prepared  for  writing,  and  he  maintained  that 
nothing  is  in  the  understanding  which  does  not 
come  through  the  senses.  This  position  is  in 
accord  with  the  popular  conceptions  as  Aristotle's 
positions  usually  are.  Plato  thinks  more  pro- 
foundly. Such  tenets  or  practicologies  are  never- 
theless allowable  in  ordinary  use  somewhat  in  the 
same  way  as  those  who  accept  the  Copernican 
theory  still  continue  to  speak  of  the  rising  and  set- 
ting of  the  sun.  I  find  indeed  that  these  usages  can 


46  LEIBNIZ. 

be  given  a  real  meaning  containing  no  error,  quite 
in  the  same  way  as  I  have  already  pointed  out  that 
we  may  truly  say  particular  substances  act  upon  one 
another.  In  this  same  sense  we  may  say  that 
knowledge  is  received  from  without  through  the 
medium  of  the  senses  because  certain  exterior  things 
contain  or  express  more  particularly  the  causes 
which  determine  us  to  certain  thoughts.  Because 
in  the  ordinary  uses  of  life  we  attribute  to  the  soul 
only  that  which  belongs  to  it  most  manifestly  and 
particularly,  and  there  is  no  advantage  in  going 
further.  When,  however,  we  are  dealing  with  the 
exactness  of  metaphysical  truths,  it  is  important  to 
recognize  the  powers  and  independence  of  the  soul 
which  extend  infinitely  further  than  is  commonly 
supposed.  In  order,  therefore,  to  avoid  misunder- 
standings it  would  be  well  to  choose  separate  terms 
for  the  two.  These  expressions  which  are  in  the 
soul  whether  one  is  conceiving  of  them  or  not  may 
be  called  ideas,  while  those  which  one  conceives  of 
or  constructs  may  be  called  conceptions,  conceptus. 
But  whatever  terms  are  used,  it  is  always  false  to 
say  that  all  our  conceptions  come  from  the  so-called 
external  senses,  because  those  conceptions  which 
I  have  of  myself  and  of  my  thoughts,  and  con- 
sequently of  being,  of  substance,  of  action,  of 
identity,  and  of  many  others  came  from  an  inner 
experience. 

XXVIII.  The  only  immediate  object  of  our  percep- 
tions which  exists  outside  of  us  is  God,  and  in  him  alone 
is  our  light. 

In  the  strictly  metaphysical  sense  no  external 
cause  acts  upon  us  excepting  God  alone,  and  he  is 


DISCOURSE  ON  METAPHYSICS.  47 

in  immediate  relation  with  us  only  by  virtue  of  our 
continual  dependence  upon  him.  Whence  it  fol- 
lows that  there  is  absolutely  no  other  external 
object  which  comes  into  contact  with  our  souls  and 
directly  excites  perceptions  in  us.  We  have  in  our 
souls  ideas  of  everything,  only  because  of  the  con- 
tinual action  of  God  upon  us,  that  is  to  say,  because 
every  effect  expresses  its  cause  and  therefore  the 
essences  of  our  souls  are  certain  expressions,  imita- 
tions or  images  of  the  divine  essence,  divine  thought 
and  divine  will,  including  all  the  ideas  which  are 
there  contained.  We  may  say,  therefore,  that  God 
is  for  us  the  only  immediate  external  object,  and 
that  we  see  things  through  him.  For  example, 
when  we  see  the  sun  or  the  stars,  it  is  God  who  gives 
to  us  and  preserves  in  us  the  ideas  and  whenever 
our  senses  are  affected  according  to  his  own  laws 
in  a  certain  manner,  it  is  he,  who  by  his  continual 
concurrence,  determines  our  thinking.  God  is  the 
sun  and  the  light  of  souls,  lumen  illuminans  omnem 
hominem  venientem  in  hunc  mundum,  although  this 
is  not  the  current  conception.  I  think  I  have 
already  remarked  that  during  the  scholastic  period 
many  believed  God  to  be  the  light  of  the  soul, 
intellectus  agens  animce  rationalis,  following  in  this 
the  Holy  Scriptures  and  the  fathers  who  were  always 
more  Platonic  than  Aristotelian  in  their  mode  of 
thinking.  The  Averroists  misused  this  conception, 
but  others,  among  whom  were  several  mystic  theo- 
logians, and  William  of  Saint  Amour,  also  I  think, 
understood  this  conception  in  a  manner  which 
assured  the  dignity  of  God  and  was  able  to  raise  the 
soul  to  a  knowledge  of  its  welfare. 


48  LEIBNIZ. 

XXIX.  Tet  we  think  directly  by  means  of  our  own 
ideas  and  not  through  God's. 

Nevertheless  I  cannot  approve  of  the  position  of 
certain  able  philosophers  who  seem  to  hold  that 
our  ideas  themselves  are  in  God  and  not  at  all  in 
us.  I  think  that  in  taking  this  position  they  have 
neither  sufficiently  considered  the  nature  of  sub- 
stance, which  we  have  just  explained,  nor  the  entire 
extension  and  independence  of  the  soul  which 
includes  all  that  happens  to  it,  and  expresses  God, 
and  with  him  all  possible  and  actual  beings  in  the 
same  way  that  an  effect  expresses  its  cause.  It  is 
indeed  inconceivable  that  the  soul  should  think 
using  the  ideas  of  something  else.  The  soul  when 
it  thinks  of  anything  must  be  affected  effectively  in 
a  certain  manner,  and  it  must  needs  have  in  itself 
in  advance  not  only  the  passive  capacity  of  being 
thus  affected,  a  capacity  already  wholly  determined, 
but  it  must  have  besides  an  active  power  by  virtue 
of  which  it  has  always  had  in  its  nature  the  marks 
of  the  future  production  of  this  thought,  and  the 
disposition  to  produce  it  at  its  proper  time.  All  of 
this  shows  that  the  soul  already  includes  the  idea 
which  is  comprised  in  any  particular  thought. 

XXX.  How  God  inclines  our  souls  without  necessitat- 
ing them;  that  there  are  no  grounds  for  complaint;  that 
we  must  not  ask  why  Judas  sinned  because  this  free  act 
is  contained  in  his  concept,  the  only  question  being  why 
Judas  the  sinner  is  admitted  to  existence,  preferably  to 
other  possible  persons;  concerning  the  original  imperfec- 
tion or  limitation  before  the  fall  and  concerning  the 
different  degrees  of  grace. 

Regarding  the  action  of  God  upon  the   human 


DISCOURSE    ON    METAPHYSICS.  49 

will  there  are  many  quite  different  considerations 
which  it  would  take  too  long  to  investigate  here. 
Nevertheless  the  following  is  what  can  be  said  in 
general.  God  in  co-operating  with  ordinary  actions 
only  follows  the  laws  which  he  has  established, 
that  is  to  say,  he  continually  preserves  and  pro- 
duces our  being  so  that  the  ideas  come  to  us  spon- 
taneously or  with  freedom  in  that  order  which  the 
concept  of  our  individual  substance  carries  with 
itself.  In  this  concept  they  can  be  foreseen  for  all 
eternity.  Furthermore,  by  virtue  of  the  decree 
which  God  has  made  that  the  will  shall  always  seek 
the  apparent  good  in  certain  particular  respects  (in 
regard  to  which  this  apparent  good  always  has  in 
it  something  of  reality  expressing  or  imitating 
God's  will),  he,  without  at  all  necessitating  our 
choice,  determines  it  by  that  which  appears  most 
desirable.  For  absolutely  speaking,  our  will  as 
contrasted  with  necessity,  is  in  a  state  of  indiffer- 
ence, being  able  to  act  otherwise,  or  wholly  to  sus- 
pend its  action,  either  alternative  being  and  remain- 
ing possible.  It  therefore  devolves  upon  the  soul 
to  be  on  guard  against  appearances,  by  means  of  a 
firm  will,  to  reflect  and  to  refuse  to  act  or  decide  in 
certain  circumstances,  except  after  mature  delibera- 
tion. It  is,  however,  true  and  has  been  assured 
from  all  eternity  that  certain  souls  will  not  employ 
their  power  upon  certain  occasions. 

But  who  could  do  more  than  God  has  done,  and 
can  such  a  soul  complain  of  anything  except  itself? 
All  these  complaints  after  the  deed  are  unjust,  inas- 
much as  they  would  have  been  unjust  before  the 
deed.  Would  this  soul  a  little  before  committing 
the  sin  have  had  the  right  to  complain  of  God  as 


50  LEIBNIZ. 

though  he  had  determined  the  sin.  Since  the  deter- 
minations of  God  in  these  matters  cannot  be  fore- 
seen, how  would  the  soul  know  that  it  was  pre- 
ordained to  sin  unless  it  had  already  committed  the 
sin?  It  is  merely  a  question  of  wishing  to  or  not 
wishing  to,  and  God  could  not  have  set  an  easier  or 
juster  condition.  Therefore  all  judges  without 
asking  the  reasons  which  have  disposed  a  man  to 
have  an  evil  will,  consider  only  how  far  this  will  is 
wrong.  But,  you  object,  perhaps  it  is  ordained 
from  all  eternity  that  I  will  sin.  Find  your  own 
answer.  Perhaps  it  has  not  been.  Now  then, 
without  asking  for  what  you  are  unable  to  know  and 
in  regard  to  which  you  can  have  no  light,  act  accord- 
ing to  your  duty  and  your  knowledge.  But,  some 
one  will  object;  whence  comes  it  then  that  this 
man  will  assuredly  do  this  sin?  The  reply  is  easy. 
It  is  that  otherwise  he  would  not  be  a  man.  For 
God  foresees  from  all  time  that  there  will  be  a 
certain  Judas,  and  in  the  concept  or  idea  of  him 
which  God  has,  is  contained  this  future  free  act. 
The  only  question,  therefore,  which  remains  is  why 
this  certain  Judas,  the  betrayer  who  is  possible  only 
because  of  the  idea  of  God,  actually  exists.  To 
this  question,  however,  we  can  expect  no  answer 
here  on  earth  excepting  to  say  in  general  that  it  is 
because  God  has  found  it  good  that  he  should  exist 
notwithstanding  that  sin  which  he  foresaw.  This 
evil  will  be  more  than  overbalanced.  God  will 
derive  a  greater  good  from  it,  and  it  will  finally 
turn  out  that  this  series  of  events  in  which  is 
included  the  existence  of  this  sinner,  is  the  most 
perfect  among  all  the  possible  series  of  events.  An 
explanation  in  every  case  of  the  admirable  econ- 


DISCOURSE    ON    METAPHYSICS.  $1 

omy  of  this  choice  cannot  be  given  while  we  are 
sojourners  on  earth.  It  is  enough  to  know  the 
excellence  without  understanding  it.  It  is  here 
that  must  be  recognized  altitudinem  divitiarum,  the 
unfathomable  depth  of  the  divine  wisdom,  without 
hesitating  at  a  detail  which  involves  an  infinite 
number  of  considerations.  It  is  clear,  however, 
that  God  is  not  the  cause  of  ill.  For  no,t  only 
after  the  loss  of  innocence  by  men,  has  original  sin 
possessed  the  soul,  but  even  before  that  there  was 
an  original  limitation  or  imperfection  in  the  very 
nature  of  all  creatures,  which  rendered  them  open 
to  sin  and  able  to  fall.  There  is,  therefore,  no  more 
difficulty  in  the  supralapsarian  view  than  there  is  in 
the  other  views  of  sin.  To  this  also,  it  seems  to 
me  can  be  reduced  the  opinion  of  Saint  Augustine 
and  of  other  authors:  that  the  root  of  evil  is  in  the 
negativity,  that  is  to  say,  in  the  lack  or  limitation 
of  creatures  which  God  graciously  remedies  by  what- 
ever degree  of  perfection  it  pleases  him  to  give. 
This  grace  of  God,  whether  ordinary  or  .extraordi- 
nary has  its  degrees  and  its  measures.  It  is  always 
efficacious  in  itself  to  produce  a  certain  proportion- 
ate effect  and  furthermore  it  is  always  sufficient  not 
only  to  keep  one  from  sin  but  even  to  effect  his 
salvation,  provided  that  the  man  co-operates  with 
that  which  is  in  him.  It  has  not  always,  however, 
sufficient  power  to  overcome  the  inclination,  for,  if 
it  did,  it  would  no  longer  be  limited  in  any  way, 
and  this  superiority  to  limitations  is  reserved  to 
that  unique  grace  which  is  absolutely  efficacious. 
This  grace  is  always  victorious  whether  through 
its  own  self  or  through  the  congruity  of  circum- 
stances. 


52  LEIBNIZ. 

XXXI.  Concerning  the  motives  of  election ;  concern- 
ing faith  foreseen  and  the  absolute  decree  and  that 
it  all  reduces  to  the  question  why  God  has  chosen  and 
resolved  to  admit  to  existence  just  such  a  possible  per- 
son, whose  concept  includes  just  such  a  sequence  of  free 
acts  and  of  free  gifts  of  grace.  This  at  once  puts  an  end 
to  all  difficulties. 

Finally,  the  grace  of  God  is  wholly  unprejudiced 
and  creatures  have  no  claim  upon  it.  Just  as  it  is 
not  sufficient  in  accounting  for  God's  choice  in  his 
dispensations  of  grace  to  refer  to  his  absolute  or 
conditional  prevision  of  men's  future  actions,  so  it 
is  also  wrong  to  imagine  his  decrees  as  absolute 
with  no  reasonable  motive.  As  concerns  foreseen 
faith  and  good  works,  it  is  very  true  that  God  has 
elected  none  but  those  whose  faith  and  charity  he 
foresees,  quos  se  fide  donaturum  praescivit.  The 
same  question,  however,  arises  again  as  to  why  God 
gives  to  some  rather  than  to  others  the  grace  of 
faith  or  of  good  works.  As  concerns  God's  ability 
to  foresee  not  only  the  faith  and  good  deeds,  but 
also  their  material  and  predisposition,  or  that  which 
a  man  on  his  part  contributes  to  them  (since  there 
are  as  truly  diversities  on  the  part  of  men  as  on 
the  part  of  grace,  and  a  man  although  he  needs  to 
be  aroused  to  good  and  needs  to  become  converted, 
yet  acts  in  accordance  with  his  temperament), — as 
regards  his  ability  to  foresee  there  are  many  who 
say  that  God,  knowing  what  a  particular  man  will 
do  without  grace,  that  is  without  his  extraordinary 
assistance,  or  knowing  at  least  what  will  be  the 
human  contribution,  resolves  to  give  grace  to  those 
whose  natural  dispositions  are  the  best,  or  at  any  rate 
are  the  least  imperfect  and  evil.  But  if  this  were  the 


DISCOURSE    ON    METAPHYSICS.  53 

case  then  the  natural  dispositions  in  so  far  as  they 
were  good  would  be  like  gifts  of  grace,  since  God 
would  have  given  advantages  to  some  over  others; 
and  therefore,  since  he  would  well  know  that  the 
natural  advantages  which  he  had  given  would  serve 
as  motives  for  his  grace  or  for  his  extraordinary 
assistance,  would  not  everything  be  reduced  to  his 
mercy?  I  think,  therefore,  that  since  we  do  not 
know  how  much  and  in  what  way  God  regards 
natural  dispositions  in  the  dispensations  of  his  grace, 
it  would  be  safest  and  most  exact  to  say,  in  accord- 
ance with  our  principles  and  as  I  have  already 
remarked,  that  there  must  needs  be  among  possible 
beings  the  person  Peter  or  John  whose  concept  or 
idea  contains  all  that  particular  sequence  of  ordi- 
nary and  extraordinary  manifestations  of  grace 
together  with  the  rest  of  the  accompanying  events 
and  circumstances,  and  that  it  has  pleased  God  to 
choose  him  among  an  infinite  number  of  persons 
equally  possible  for  actual  existence.  When  we 
have  said  this  there  seems  nothing  left  to  ask,  and 
all  difficulties  vanish.  For  in  regard  to  that  great 
and  ultimate  question  why  it  has  pleased  God  to 
choose  him  among  so  great  a  number  of  possible 
persons,  it  is  surely  unreasonable  to  demand  more 
than  the  general  reasons  which  we  have  given. 
The  reasons  in  detail  surpass  our  ken.  Therefore, 
instead  of  postulating  an  absolute  decree,  which 
being  without  reason  would  be  unreasonable,  and 
instead  of  postulating  reasons  which  do  not  succeed 
in  solving  the  difficulties  and  in  turn  have  need 
themselves  of  reasons,  it  will  be  best  to  say  with 
St.  Paul  that  there  are  for  God's  choice  certain 
great  reasons  of  wisdom  and  congruity  which  he 


54  LEIBNIZ. 

follows,  which  reasons,  however,  are  unknown  to 
mortals  and  are  founded  upon  the  general  order, 
whose  goal  is  the  greatest  perfection  of  the  world. 
This  is  what  is  meant  when  the  motives  of  God's 
glory  and  of  the  manifestation  of  his  justice  are 
spoken  of,  as  well  as  when  men  speak  of  his  mercy, 
and  his  perfection  in  general;  that  immense  vastness 
of  wealth,  in  fine,  with  which  the  soul  of  the  same 
St.  Paul  was  to  thrilled. 


XXXII.   Usefulness  of  these  principles  in  matters  of 

piety  and  of  religion. 
.or 

*  W-       In  addition  it  seems  that  the  thoughts  which  we 

c^ "\  have  just  explained  and  particularly  the  great  prin- 
ciple of  the  perfection  of  God's  operations  and  the 
concept  of  substance  which  includes  all  its  changes 
with  all  its  accompanying  circumstances,  far  from 
injuring,  serve  rather  to  confirm  religion,  serve  to 
dissipate  great  difficulties,  to  inflame  souls  with  a 
divine  love  and  to  raise  the  mind  to  a  knowledge 
of  incorporeal  substances  much  more  than  the 
present-day  hypotheses.  For  it  appears'  clearly 
that  all  other  substances  depend  upon  God  just  as 
our  thoughts  emanate  from  our  own  substances; 
that  God  is  all  in  all  and  that  he  is  intimately  united 
to  all  created  things,  in  proportion  however  to  their 
perfection;  that  it  is  he  alone  who  determines  them 
from  without  by  his  influence,  and  if  to  act  is  to 
determine  directly,  it  may  be  said  in  metaphysical 
language  that  God  alone  acts  upon  me  and  he  alone 
causes  me  to  do  good  or  ill,  other  substances  con- 
tributing only  because  of  his  determinations; 
because  God,  who  takes  all  things  into  considera- 


DISCOURSE    ON    METAPHYSICS.  55 

tion,  distributes  his  bounties  and  compels  created 
beings  to  accommodate  themselves  to  one  another. 
Thus  God  alone  constitutes  the  relation  or  commu- 
nication between  substances.  It  is  through  him  that 
the  phenomena  of  the  one  meet  and  accord  with  the 
phenomena  of  the  others,  so  that  there  may  be  a 
reality  in  our  perceptions.  In  common  parlance, 
however,  an  action  is  attributed  to  particular  causes 
in  the  sense  that  I  have  explained  above  because  it 
is  not  necessary  to  make  continual  mention  of  the 
universal  cause  when  speaking  of  particular  cases. 
It  can  be  seen  also  that  every  substance  has  a  per- 
fect spontaneity  (which  becomes  liberty  with  intel- 
ligent substances).  Everything  which  happens  to  it 
is  a  consequence  of  its  idea  or  its  being  and  noth- 
ing determines  it  except  God  only.  It  is  for  this 
reason  that  a  person  of  exalted  mind  and  revered 
saintliness  may  say  that  the  soul  ought  often  to 
think  as  if  there  were  only  God  and  itself  in  the 
world.  Nothing  can  make  us  hold  to  immortality 
more  firmly  than  this  independence  and  vastness  of 
the  soul  which  protects  it  completely  against  exte- 
rior things,  since  it  alone  constitutes  our  universe 
and  together  with  God  is  sufficient. for  itself.  It  is 
as  impossible  for  it  to  perish  save  through  annihila- 
tion as  it  is  impossible  for  the  universe  to  destroy 
itself,  the  universe  whose  animate  and  perpetual 
expression  it  is.  Furthermore,  the  changes  in  this 
extended  mass  which  is  called  our  body  cannot  pos- 
sibly affect  the  soul  nor  can  the  dissipation  of  the 
body  destroy  that  which  is  indivisible. 


LEIBNIZ. 

XXXIII.  Explanation  of  the  relation  between  the 
soul  and  the  body,  a  matter  which  has  been  regarded  as 
inexplicable  or  else  as  miraculous;  concerning  the  origin 
of  confused  perceptions. 

We  can  also  see  the  explanation  of  that  great 
mystery  "the  union  of  the  soul  and  the  body,"  that 
is  to  say  how  it  comes  about  that  the  passions  and 
actions  of  the  one  are  accompanied  by  the  actions 
and  passions  or  else  the  appropriate  phenomena  of 
the  other.  For  it  is  not  possible  to  conceive  how 
one  can  have  an  influence  upon  the  other  and  it  is 
unreasonable  to  have  recourse  at  once  to  the  extraor- 
dinary intervention  of  the  universal  cause  in  an 
ordinary  and  particular  case.  The  following,  how- 
ever, is  the  true  explanation.  We  have  said  that 
everything  which  happens  to  a  soul  or  to  any  sub- 
stance is  a  consequence  of  its  concept;  hence  the 
idea  itself  or  the  essence  of  the  soul  brings  it  about 
that  all  of  its  appearances  or  perceptions  should  be 
born  out  of  its  nature  and  precisely  in  such  a  way 
that  they  correspond  of  themselves  to  that  which 
happens  in  the  universe  at  large,  but  more  partic- 
ularly and  more  perfectly  to  that  which  happens  in 
the  body  associated  with  it,  because  it  is  in  a  partic- 
ular way  and  only  for  a  certain  time  according  to 
the  relation  of  other  bodies  to  its  own  body  that  the 
soul  expresses  the  state  of  the  universe.  This  last 
fact  enables  us  to  see  how  our  body  belongs  to  us, 
without,  however,  being  attached  to  our  essence. 
I  believe  that  those  who  are  careful  thinkers  will 
decide  favorably  for  our  principles  because  of  this 
single  reason,  viz.,  that  they  are  able  to  see  in  what 
consists  the  relation  between  the  soul  and  the  body, 
a  parallelism  which  appears  inexplicable  in  any 


DISCOURSE    ON    METAPHYSICS.  57 

other  way.  We  can  also  see  that  the  perceptions  of 
our  senses  even  when  they  are  clear  must  necessarily 
contain  certain  confused  elements,  for  as  all  the 
bodies  in  the  universe  are  in  sympathy,  ours  receives 
the  impressions  of  all  the  others,  and  while  our 
senses  respond  to  everything,  our  soul  cannot  pay 
attention  to  every  particular.  That  is  why  our  con- 
fused sensations  are  the  result  of  a  variety  of  per- 
ceptions This  variety  is  infinite.  It  is  almost  like 
the  confused  murmuring  which  is  heard  by  those 
who  approach  the  shore  of  a  sea.  It  comes  from 
the  continual  beatings  of  innumerable  waves.  If 
now,  out  of  many  perceptions  which  do  not  at  all 
fit  together  to  make  one,  no  particular  one  percep- 
tion surpasses  the  others,  and  if  they  make  impres- 
sions about  equally  strong  or  equally  capable  of 
holding  the  attention  of  the  soul,  they  can  be  per- 
ceived only  confusedly. 


XXXIV.  Concerning  the  difference  between  spirits 
and  other  substances,  souls  or  substantial  forms;  that  the 
immortality  which  men  desire  includes  memory. 

Supposing  that  the  bodies  which  constitute  a 
unum  per  se,  as  human  bodies,  are  substances,  and 
have  substantial  forms,  and  supposing  that  animals 
have  souls,  we  are  obliged  to  grant  that  these  souls 
and  these  substantial  forms  cannot  entirely  perish, 
any  more  than  can  the  atoms  or  the  ultimate  ele- 
ments of  matter,  according  to  the  position  of  other 
philosophers;  for  no  substance  perishes,  although 
it  may  become  very  different.  Such  substances 
also  express  the  whole  universe,  although  more 
imperfectly  than  do  spirits.  The  principle  differ- 


58  LEIBNIZ. 

ence,  however,  is  that  they  do  not  know  that  they 
are,  nor  what  they  are.  Consequently,  not  being 
able  to  reason,  they  are  unable  to  discover  necessary 
and  universal  truths.  It  is  also  because  they  do  not 
reflect  regarding  themselves  that  they  have  no 
moral  qualities,  whence  it  follows  that  undergoing 
a  thousand  transformations,  as  we  see  a  caterpillar 
change  into  a  butterfly,  the  result  from  a  moral  or 
practical  standpoint  is  the  same  as  if  we  said  that 
they  perished  in  each  case,  and  we  can  indeed  say 
it  from  the  physical  standpoint  in  the  same  way 
that  we  say  bodies  perish  in  their  dissolution.  But 
the  intelligent  soul,  knowing  that  it  is  and  having 
the  ability  to  say  that  word  "I"  so  full  of  meaning, 
not  only  continues  and  exists,  metaphysically  far 
more  certainly  than  do  the  others,  but  it  remains 
the  same  from  the  moral  standpoint,  and  constitutes 
the  same  personality,  for  it  is  its  memory  or  knowl- 
edge of  this  ego  which  renders  it  open  to  punish- 
ment and  reward.  Also  the  immortality  which  is 
required  in  morals  and  in  religion  does  not  consist 
merely  in  this  perpetual  existence,  which  pertains 
to  all  substances,  for  if  in  addition  there  were  no 
remembrance  of  what  -one  had  been,  immortality 
would  not  be  at  all  desirable.  Suppose  that  some 
individual  could  suddenly  become  King  of  China 
on  condition,  however,  of  forgetting  what  he  had 
been,  as  though  being  born  again,  would  it  not 
amount  to  the  same  practically,  or  as  far  as  the 
effects  could  be  perceived,  as  if  the  individual  were 
annihilated,  and  a  king  of  China  were  the  same 
instant  created  in  his  place?  The  individual  would 
have  no  reason  to  desire  this. 


DISCOURSE   ON    METAPHYSICS.  59 

XXXV.  The  excellence  of  spirits;  that  God  considers 
them  preferable  to  other  creatures;  that  the  spirits  ex- 
press God  rather  than  the  world,  while  other  simple 
substances  express  the  world  rather  than  God. 

In  order,  however,  to  prove  by  natural  reasons 
that  God  will  preserve  forever  not  only  our  sub- 
stance, but  also  our  personality,  that  is  to  say  the 
recollection  and  knowledge  of  what  we  are  (although 
the  distinct  knowledge  is  sometimes  suspended 
during  sleep  and  in  swoons)  it  is  necessary  to  join 
to  metaphysics  moral  considerations.  God  must  be 
considered  not  only  as  the  principle  and  the  cause 
of  all  substances  and  of  all  existing  things,  but  also 
as  the  chief  of  all  persons  or  intelligent  substances, 
as  the  absolute  monarch  of  the  most  perfect  city  or 
republic,  such  as  is  constituted  by  all  the  spirits 
together  in  the  universe,  God  being  the  most  com- 
plete of  all  spirits  at  the  same  time  that  he  is  great- 
est of  all  beings.  For  assuredly  the  spirits  are  the 
most  perfect  of  substances  and  best  express  the 
divinity.  Since  all  the  nature,  purpose,  virtue  and 
function  of  substances  is,  as  has  been  sufficiently 
explained,  to  express  God  and  the  universe,  there 
is  no  room  for  doubting  that  those  substances  which 
give  the  expression,  knowing  what  they  are  doing 
and  which  are  able  to  understand  the  great  truths 
about  God  and  the  universe,  do  express  God  and  the 
universe  incomparably  better  than  do  those  natures 
which  are  either  brutish  and  incapable  of  recogniz- 
ing truths,  or  are  wholly  destitute  of  sensation  and 
knowledge.  The  difference  between  intelligent 
substances  and  those  which  are  not  intelligent  is 
quite  as  great  as  between  a  mirror  and  one  who  sees. 
As  God  is  himself  the  greatest  and  wisest  of  spirits 


60  LEIBNIZ. 

it  is  easy  to  understand  that  the  spirits  with  which 
he  can,  so  to  speak,  enter  into  conversation  and 
even  into  social  relations  by  communicating  to 
them  in  particular  ways  his  feelings  and  his  will  so 
that  they  are  able  to  know  and  love  their  benefac- 
tor, must  be  much  nearer  to  him  than  the  rest  of 
created  things  which  may  be  regarded  as  the  instru- 
ments of  spirits.  In  the  same  way  we  see  that  all 
wise  persons  consider  far  more  the  condition  of  a 
man  than  of  anything  else  however  precious  it  may 
be;  and  it  seems  that  the  greatest  satisfaction  which 
a  soul,  satisfied  in  other  respects,  can  have  is  to  see 
itself  loved  by  others.  However,  with  respect  to 
God  there  is  this  difference  that  his  glory  and  our 
worship  can  add  nothing  to  his  satisfaction,  the 
recognition  of  creatures  being  nothing  but  a  conse- 
quence of  his  sovereign  and  perfect  felicity  and 
being  far  from  contributing  to  it  or  from  causing 
it  even  in  part.  Nevertheless,  that  which  is  reason- 
able in  finite  spirits  is  found  eminently  in  him  and 
as  we  praise  a  king  who  prefers  to  preserve  the  life 
of  a  man  before  that  of  the  most  precious  and  rare 
of  his  animals,  we  should  not  doubt  that  the  most 
enlightened  and  most  just  of  all  monarchs  has  the 
same  preference. 

XXXVI.  God  is  the  monarch  of  the  most  perfect  re* 
public  composed  of  all  the  spirits,  and  the  happiness  of 
this  city  of  God  is  his  principal  purpose. 

Spirits  are  of  all  substances  the  most  capable  of 
perfection  and  their  perfections  are  different  in  this 
that  they  interfere  with  one  another  the  least,  or 
rather  they  aid  one  another  the  most,  for  only  the 
most  virtuous  can  be  the  most  perfect  friends. 


DISCOURSE   ON    METAPHYSICS.  6l 

Hence  it  follows  that  God  who  in  all  things  has  the 
greatest  perfection  will  have  the  greatest  care  for 
spirits  and  will  give  not  only  to  all  of  them  in 
general,  but  even  to  each  one  in  particular  the 
highest  perfection  which  the  universal  harmony  will 
permit.  We  can  even  say  that  it  is  because  he  is  a. 
spirit  that  God  is  the  originator  of  existences,  for 
if  he  had  lacked  the  power  of  will  to  choose  what 
is  best,  there  would  have  been  no  reason  why  one 
possible  being  should  exist  rather  than  any  other. 
Therefore  God's  being  a  spirit  himself  dominates 
all  the  consideration  which  he  may  have  toward 
created  things.  Spirits  alone  are  made  in  his 
image,  being  as  it  were  of  his  blood  or  as  children 
in  the  family,  since  they  alone  are  able  to  serve 
him  of  free  will,  and  to  act  consciously  imitating 
the  divine  nature.  A  single  spirit  is  worth  a  whole 
world,  because  it  not  only  expresses  the  whole 
world,  but  it  also  knows  it  and  governs  itself  as 
does  God.  In  this  way  we  may  say  that  though 
every  substance  expresses  the  whole  universe,  yet 
the  other  substances  express  the  world  rather  than 
God,  while  spirits  express  God  rather  than  the 
world.  This  nature  of  spirits,  so  noble  that  it 
enables  them  to  approach  divinity  as  much  as  is 
possible  for  created  things,  has  as  a  result  that  God 
derives  infinitely  more  glory  from  them  than  from 
the  other  beings,  or  rather  the  other  beings  furnish 
to  spirits  the  material  for  glorifying  him.  This 
moral  quality  of  God  which  constitutes  him  Lord 
and  Monarch  of  spirits  influences  him  so  to  speak 
personally  and  in  a  unique  way.  It  is  through  this 
that  he  humanizes  himself,  that  he  is  willing  to 
suffer  anthropologies,  and  that  he  enters  into  social 


6a  LEIBNIZ. 

relations  with  us  and  this  consideration  is  so  dear 
to  him  that  the  happy  and  prosperous  condition  of 
his  empire  which  consists  in  the  greatest  possible 
felicity  of  its  inhabitants,  becomes  supreme  among 
his  laws.  Happiness  is  to  persons  what  perfection 
is  to  beings.  And  if  the  dominant  principle  in  the 
existence  of  the  physical  world  is  the  decree  to 
give  it  the  greatest  possible  perfection,  the  primary 
purpose  in  the  moral  world  or  in  the  city  of  God 
which  constitutes  the  noblest  part  of  the  universe 
ought  to  be  to  extend  the  greatest  happiness  pos- 
sible. We  must  not  therefore  doubt  that  God  has 
so  ordained  everything  that  spirits  not  only  shall 
live  forever,  because  this  is  unavoidable,  but  that 
they  shall  also  preserve  forever  their  moral 
quality,  so  that  his  city  may  never  lose  a  person, 
quite  in  the  same  way  that  the  world  never  loses  a 
substance.  Consequently  they  will  always  be  con- 
scious of  their  being,  otherwise  they  would  be  open 
to  neither  reward  nor  punishment,  a  condition 
which  is  the  essence  of  a  republic,  and  above  all  of 
the  most  perfect  republic  where  nothing  can  be 
neglected.  In  fine,  God  being  at  the  same  time 
the  most  just  and  the  most  debonnaire  of  monarchs, 
and  requiring  only  a  good  will  on  the  part  of  men, 
provided  that  it  be  sincere  and  intentional,  his  sub- 
jects cannot  desire  a  better  condition.  To  render  them 
perfectly  happy  he  desires  only  that  they  love  him. 

XXXVII.  Jesus  Christ  has  revealed  to  men  the  mys- 
tery and  the  admirable  laws  of  the  kingdom  of  heaven, 
and  the  greatness  of  the  supreme  happiness  which  God 
has  prepared  for  those  who  love  him. 

The  ancient  philosophers  knew  very  little  of  these 


DISCOURSE    ON    METAPHYSICS.  63 

important  truths.  Jesus  Christ  alone  has  expressed 
them  divinely  well,  and  in  a  way  so  clear  and  sim- 
ple that  the  dullest  minds  have  understood  them. 
His  gospel  has  entirely  changed  the  face  of  human 
affairs.  It  has  brought  us  to  know  the  kingdom  of 
heaven,  or  that  perfect  republic  of  spirits  which 
deserves  to  be  called  the  city  of  God.  He  it  is  who 
has  discovered  to  us  its  wonderful  laws.  He  alone 
has  made  us  see  how  much  God  loves  us  and  with 
what  care  everything  that  concerns  us  has  been 
provided  for;  how  God,  inasmuch  as  he  cares  for 
the  sparrows,  will  not  neglect  reasoning  beings,  who 
are  infinitely  more  dear  to  him;  how  all  the  hairs  of 
our  heads  are  numbered;  how  heaven  and  earth  may 
pass  away  but  the  word  of  God  and  that  which 
belongs  to  the  means  of  our  salvation  will  not  pass 
away;  how  God  has  more  regard  for  the  least  one 
among  intelligent  souls  than  for  the  whole  machin- 
ery of  the  world;  how  we  ought  not  to  fear  those 
who  are  able  to  destroy  the  body  but  are  unable  to 
destroy  the  soul,  since  God  alone  can  render  the  soul 
happy  or  unhappy;  and  how  the  souls  of  the  right- 
eous are  protected  by  his  hand  against  all  the 
upheavals  of  the  universe,  since  God  alone  is  able 
to  act  upon  them;  how  none  of  our  acts -are  forgot- 
ten; how  everything  is  to  be  accounted  for;  even 
careless  words  and  even  a  spoonful  of  water  which 
is  well  used;  in  fact  how  everything  must  result  in 
the  greatest  welfare  of  the  good,  for  then  shall  the 
righteous  become  like  suns  and  neither  our  sense 
nor  our  minds  have  ever  tasted  of  anything 
approaching  the  joys  which  God  has  laid  up  for 
those  that  love  him. 


CORRESPONDENCE 

RELATING   TO   THE   METAPHYSICS. 


CORRESPONDENCE   RELATING  TO 
THE   METAPHYSICS. 

I. 

Leibniz  to  Count  Ernst  von  Hessen-Rheinfels, 

i/i i  Feb.,  1686. 

.  .  .  Being  at  a  place  lately  for  several  days  with 
nothing  to  do,  I  wrote  out  a  short  discourse  on 
Metaphysics  on  which  I  should  be  very  glad  to  have 
the  opinion  of  Mons.  Arnaud.*  For  the  questions 
in  regard  to  grace,  in  regard  to  the  relations  of  God 
with  created  beings,  in  regard  to  the  nature  of  mir- 
acles, the  cause  of  sin,  the  origin  of  evil,  the 
immortality  of  the  soul,  ideas,  etc.,  are  discussed  in 
a  way  which  seems  to  offer  new  points  of.  approach 
fitted  to  clear  up  some  great  difficulties.  I  enclose 
herewith  a  summary  of  the  articles  which  it  con- 
tains, as  I  have  not  had  time  to  make  a  clean  copy 
of  the  whole. 

I  therefore  beg  Your  Serene  Highness  to  send  him 
this  summary,  requesting  him  to  look  it  over  and 
give  his  judgment  upon  it.  For,  as  he  excels 
equally  in  Theology  and  in  Philosophy,  in  erudition 
and  in  power  of  thought,  I  know  of  no  one  who  is 
better  fitted  to  give  an  opinion  upon  it.  I  am  very 
desirous  to  have  a  critic  as  careful,  as  enlightened 
and  as  open  to  reason  as  is  Monsieur  Arnaud,  being 
myself  also  a  person  the  most  disposed  in  the  world 
to  submit  to  reasoning. 

*  Leibniz  always  used  the  form  Arnaud. — Trans. 

6? 


68  CORRESPONDENCE. 

Perhaps  Mons.  Arnaud  will  not  find  this  outline 
wholly  unworthy  of  his  consideration,  especially 
since  he  has  been  somewhat  occupied  in  the  exam- 
ination of  these  matters.  If  he  finds  obscurities  I 
will  explain  myself  sincerely  and  frankly,  and  if  he 
finds  me  worthy  indeed  of  his  instruction  I  shall  try 
to  behave  in  such  a  way  that  he  shall  find  no  cause 
for  being  dissatisfied  on  that  point.  I  beg  Your 
Serene  Highness  to  enclose  this  with  the  summary 
which  I  am  sending  and  to  forward  them  both  to 
Mons.  Arnaud. 


SUMMARY  OF  THE  DISCOURSE  ON  META- 
PHYSICS 

1.  Concerning  the  divine  perfection  and  that  God 
does  everything  in  the  most  desirable  way. 

2.  Against  those  who  hold  that  there  is  in  the 
works  of  God  no  goodness,  or  that  the  principles  of 
goodness  and  beauty  are  arbitrary. 

3.  Against  those  who  think  that  God  might  have 
made  things  better  than  he  has. 

4.  That  love  for  God  demands  on  our  part  com- 
plete  satisfaction   with   and   acquiescence    in   that 
which  he  has  done. 

5.  In  what  the  principles  of  the  perfection  of  the 
divine  conduct  consist  and  that  the  simplicity  of 
the   means    counterbalances    the    richness    of    the 
effects. 

6.  That  God  does  nothing  which  is  not  orderly 
and   that   it   is   not   even   possible   to   conceive  of 
events  which  are  not  regular. 

7.  That  miracles   conform    to   the   general  order 
although  they  go  against  the   subordinate   regula- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  69 

tions;  concerning  that  which  God  desires  or  permits 
and  concerning  general  and  particular  intentions. 

8.  In  order  to  distinguish  between  the  activities 
of  God  and  the  activities  of  created  things,  we  must 
explain  the  conception  of  an  individual  substance. 

9.  That  every  individual  substance  expresses  the 
whole  universe  in  its  own  manner,  and  that  in  its  full 
concept   is    included   all    its    experiences   together 
with  all  the  attendant  circumstances  and  the  whole 
sequence  of  exterior  events. 

10.  That  the  belief  in  substantial  forms  has  a  cer- 
tain basis,  in  fact  but  that  these  forms   effect  no 
changes  in  the  phenomena  and  must  not  be  employed 
for  the  explanation  of  particular  events. 

11.  That  the  opinions  of  the  theologians  and  of 
the  so-called  scholastic  philosophers  are  not  to  be 
wholly  despised. 

12.  That  the  conception  of  the  extension  of   a 
body  is  in  a  way  imaginary  and  does  not  constitute 
the  substance  of  the  body. 

13.  As   the    individual  concept   of    each    person 
includes   once   for  all  everything  which   can   ever 
happen  to  him,  in   it  can  be  seen  a  priori  the  evi- 
dences or  the  reasons  for  the  reality  of  each  event 
and  why  one  happened  sooner  than  the  other.     But 
these    events,    however   certain,    are     nevertheless 
contingent  being  based  on  the  free  choice  of  God 
and  of  his  creatures.     It  is  true  that  their  choices 
always  have  their  reasons  but  they  incline  to  the 
choices  under  no  compulsion  of  necessity. 

14.  God  produces  different  substances  according 
to  the  different  views  which   he  has  of  the  world 
and  by   the    intervention  of  God  the   appropriate 
nature  of  each  substance  brings  it  about  that  what 


7O  CORRESPONDENCE. 

happens  to  one  corresponds  to  what  happens  to  all 
the  others  without,  however,  their  acting  upon  one 
another  directly. 

15.  The    action    of    one    finite    substance    upon 
another  consists  only  in  the  increase  in  the  degree 
of  the   expression   of   the   first    combined   with   a 
decrease  in  that  of  the  second,  in  so  far  as  God  has 
in   advance   fashioned   them    so   that   they  should 
accord. 

16.  The  extraordinary  intervention  of  God  is  not 
excluded    in   that   which    our    particular    essences 
express   because   this    expression     includes    every- 
thing.    Such  intervention  however  goes  beyond  the 
power    of    our    natural    being    or    of   our   distinct 
expression  because   these   are  finite  and  follow  cer- 
tain subordinate  regulations. 

17.  An  example  of  a  subordinate  regulation  in  the 
law  of  nature  which  demonstrates  that  God  always 
preserves  the  same  amount   of   force   but  not  the 
same  quantity  of  motion;    against    the  Cartesians 
and  many  others. 

18.  The  distinction  between  force  and  the  quantity 
of  motion   is,    among  other    reasons,    important  as 
showing  that  we  must  have  recourse  to  metaphysical 
considerations  in  addition  [to  discussions  of  exten- 
sion, if  we  wish  to  explain  the  phenomena  of  matter. 

19.  The  utility  of  final  causes  in  physics. 

20.  A   noteworthy    disquisition    by  Socrates    in 
Plato's  Phaedo  against  the  philosophers  who  were 
too  materialistic. 

21.  If  the  mechanical  laws  depended  upon  geom- 
etry alone  without  metaphysical  influences,  the  phe- 
nomena would  be  very  different  from  what  they  are. 

22.  Reconciliation  of  the  two  methods  of  expla- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  71 

nation,  the  one  using  final  causes  and  the  other  effi- 
cient causes,  thus  satisfying  both  those  who  explain 
nature  mechanicariy  and  also  those  who  have 
recourse  to  incorporeal  natures. 

23.  Returning  to  immaterial  substances  we  explain 
how  God  acts  upon  the  understanding  of  spirits,  and 
ask  whether  one  always  keeps  the  idea  of  what  he 
thinks  about. 

24.  What   clear   and   obscure,   distinct   and   con- 
fused,    adequate    and     inadequate,     intuitive    and 
assumed  knowledge   is,  and  the  definition  of  nom- 
inal, real,  causal  and  essential. 

25.  In  what  cases   knowledge   is  added  to  mere 
contemplation  of  the  idea. 

26.  Ideas  are  all   stored  up  within  us.      Plato's 
doctrine  of  reminiscence. 

27.  In  what  respect  our  souls  can  be  compared  to 
blank  tablets  and  how  conceptions  are  derived  from 
the  senses. 

28.  The  only  immediate  object  of  our  perceptions 
which  exists  outside  of  us  is  God  and  in  him  alone 
is  our  light. 

29.  Yet  we  think  directly  by  means  of  our  own 
ideas  and  not  through  God's. 

30.  How  God   inclines  our  souls  without  necessi- 
tating them;  that  there  are    no  grounds  for  com- 
plaint; that   we   must   not    ask   why  Judas   sinned 
because  this  free  act   is  contained  in  his  concept, 
the  only  question    being  why  Judas  the   sinner  is 
admitted  to  existence,  preferably  to  other  possible 
persons;   concerning  the   original    imperfection   or 
limitation  before  the  fall  and  concerning  the  differ- 
ent degrees  of  grace. 

31.  The  motives  for  election,  faith  foreseen,  par- 


72  CORRESPONDENCE. 

tial  knowledge,  the  absolute  decree  and  that  the 
whole  inquiry  is  reduced  to  the  question  why  God 
has  chosen  and  resolved  to  admit  to  existence  such 
a  possible  person  whose  concept  involves  such  a 
sequence  of  gifts  of  grace  and  of  free  acts.  This  at 
once  overcomes  all  the  difficulties. 

32.  Applicability  of  these  principles  in  matters  of 
piety  and  of  religion. 

33.  Explanation  of  the  inter-relation  of  soul  and 
body  which  has  been  usually  considered  inexplica- 
ble and  miraculous;  also  concerning  the  origin  of 
confused  perceptions. 

34.  The  difference  between  spirits  and  other  sub- 
stances,  souls   or   substantial    forms,   and   that   the 
immortality  which  people  wish  for  includes  remem- 
brance. 

35.  Excellence   of   spirits;    that   God    considers 
them  preferably  to  the  other  created  things;  that 
spirits   express    God    rather  than  the  world   while 
other  simple  substances  express  rather  the  world 
than  God. 

36.  God  is  the  monarch  of  the  most  perfect  repub- 
lic  which    is  composed  of  all  the  spirits,  and  the 
felicity  of  this  city  of  God  is  his  principal  purpose. 

37.  Jesus  Christ  has  disclosed  to  men  the  mystery 
and  the  admirable  laws  of  the  Kingdom  of  Heaven 
and  the  greatness  of  the  supreme  happiness  which 
God  has  prepared  for  those  who  love  him. 

II 

Arnauld  to  Count  Ernst  von  Hessen-Rheinfels. 

March  13,  1686. 

I  have  received,    Monseigneur,   the  metaphysical 
thoughts  which  Your  Highness  sent  me  from  Mr. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  73 

Leibniz  as  a  witness  of  his  affection  and  his  esteem 
for  which  I  am  very  grateful  to  him.  But  I 
have  been  so  busy  ever  since  that  only  within  the 
last  three  days  have  I  been  able  to  read  his  mis- 
sive. 

And  at  the  present  time  I  have  such  a  bad  cold 
that  all  that  I  can  do  now  is  to  tell  Your  Highness 
in  a  couple  of  words  that  I  find  in  his  thoughts  so 
many  things  which  frightened  me  and  which  if  I 
am  not  mistaken  almost  all  men  would  find  so  star- 
tling that  I  cannot  see  any  utility  in  a  treatise  which 
would  be  evidently  rejected  by  everybody. 

I  will  instance  for  example  what  is  said  in  Article 
13:  That  the  individual  concept  of  every  person 
involves  once  for  all  everything  which  will  ever 
happen  to  him,  etc.  If  this  is  so,  God  was  free  to 
create  or  not  to  create  Adam,  but  supposing  he 
decided  to  create  him,  all  that  has  since  happened 
to  the  human  race  or  which  will  ever  happen  to  it 
has  occurred  and  will  occur  by  a  necessity  more 
than  fatal.  For  the  individual  concept  of  Adam 
involved  that  he  would  have  so  many  children  and 
the  individual  concepts  of  these  children  involved 
all  that  they  would  do  and  all  the  children  that 
they  would  have;  and  so  on.  God  has  therefore  no 
more  liberty  in  regard  to  all  that,  provided  he 
wished  to  create  Adam,  than  he  was  free  to  create 
a  nature  incapable  of  thought,  supposing  that  he 
wished  to  create  me.  I  am  not  in  a  position  to 
speak  of  this  at  greater  length,  but  Mr.  Leibniz 
will  understand  my  meaning  and  it  is  possible  that 
he  will  find  no  difficulties  in  the  consequence  which 
I  have  drawn.  If  he  finds  none,  however,  he  has 
reason  to  fear  that  he  will  be  alone  in  his  position, 


74  CORRESPONDENCE. 

and  were  I  wrong  in  this  last  statement  I  should  be 
still  sorrier. 

I  cannot  refrain  from  expressing  to  Your  High- 
ness my  sorrow  at  his  attachment  to  those  opinions, 
which  he  has  indeed  felt  could  hardly  be  permitted 
in  the  Catholic  Church.  The  Catholic  Church  would 
prohibit  his  entertaining  them,  and  it  is  apparently 
this  attachment  that  has  prevented  his  entering  the 
fold,  notwithstanding  the  fact  that  Your  Highness, 
if  I  remember  rightly,  brought  him  to  recognize  that 
there  was  no  reasonable  doubt  as  to  its  being  the 
true  church.*  Would  it  not  be  better  for  him  to 
leave  those  metaphysical  speculations  which  can 
be  of  utility  neither  to  himself  nor  to  others,  in 
order  to  apply  himself  seriously  to  the  most  im- 
portant matter  he  can  ever  undertake,  namely, 
to  assure  his  salvation,  by  entering  into  the 
Church  from  which  new  sects  can  form  only  by 
rendering  themselves  schismatic?  I  read  yesterday 
by  chance  one  of  Saint  Augustine's  letters  in  which 
he  answers  various  questions  that  were  put  forward 
by  a  Pagan  who  showed  a  desire  to  become  a  Chris- 
tian but  who  always  postponed  doing  so.  He  says, 
at  the  end,  what  may  be  applied  to  our  friend 
"There  are  numberless  problems  which  are  not  to 
be  solved  before  one  has  faith  and  will  not  be  solved 
in  life  without  faith." 

Ill 
Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

April  12,  1686. 
I  do  not  know  what  to  say  to  M.  A.'s  letter,  and 

*  Leibniz  remarks  on  the  margin  of  Arnauld's  letter:  "I  have 
never  endorsed  this  sentiment."  Interesting  as  indicating 
Leibniz's  attitude  toward  Catholicism. — Editor. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  75 

I  never  should  have  thought  that  a  person  whose 
reputation  is  so  great  and  so  real  and  from  whom 
we  have  such  excellent  Reflections  on  Morals  and 
Logic  would  be  so  precipitate  in  his  judgments. 
After  this  instance  I  am  not  surprised  that  some 
are  angry  at  him.  Nevertheless  I  think  it  well  to 
be  patient  at  times  under  the  ill  humor  of  one  whose 
merit  is  extraordinary,  provided  his  acts  have  no 
serious  results  and  I  believe  that  a  judicious  reply 
may  dissipate  a  prejudice  ill-founded.  I  anticipate 
this  justice  in  M.  A. 

Whatever  reason,  however,  I  may  have  for  com- 
plaint, I  desire  to  suppress  all  reflections  which  are 
not  essential  to  the  matter  in  hand  and  which 
might  serve  to  increase  the  ill-feeling,  but  I  hope 
he  will  use  the  same  moderation,  in  case  he  has  the 
graciousness  to  act  as  my  instructor.  I  am  only 
able  to  assure  him  that  he  is  quite  mistaken  in  cer- 
tain of  his  conjectures,  because  people  of  good  sense 
have  judged  otherwise  regarding  my  positions,  and 
that  notwithstanding  their  encouragement  I  have 
not  been  over  quick  in  publishing  anything  upon 
abstract  subjects  which  are  to  the  taste  of  few  peo- 
ple, inasmuch  as  the  public  even  has  as  yet  heard 
almost  nothing  in  regard  to  certain  more  plausible 
discoveries  which  I  made  several  years  ago. 

I  have  written  down  these  Meditations  only  in 
order  to  profit  for  my  own  sake  by  the  criticisms  of 
more  able  thinkers  and  in  order  to  receive  confi- 
dence or  correction  in  the  investigation  of  these 
most  important  truths.  It  is  true  that  some  per- 
sons of  intelligence  have  found  my  opinions  accept- 
able, but  I  should  be  the  first  to  warn  them  if  I  thought 
there  were  the  slightest  evil  effects  from  them. 


76  CORRESPONDENCE. 

This  declaration  is  sincere,  and  this  will  not  be 
the  first  time  that  I  have  profited  by  the  instruc- 
tion of  enlightened  persons.  This  is  why  I  shall 
assuredly  be  under  great  obligations  to  M.  A.  in 
case  I  merit  his  having  the  goodness  to  deliver  me 
from  the  errors  which  he  thinks  dangerous  and  of 
which,  I  declare  it  in  good  faith,  I  am  unable  to 
see  the  evil.  But  I  hope  that  he  will  use  modera- 
tion, and  that  he  will  do  me  justice,  because  men 
deserve  at  least  that  no  wrong  be  done  to  them 
through  precipitate  judgments. 

He  chooses  one  of  my  theses  to  show  that  it  is 
dangerous.  But  either  I  am  incapable  for  the 
present  of  understanding  the  difficulty  or  else  there 
is  none  in  it.  This  has  enabled  me  to  recover  from 
my  surprise  and  has  made  me  think  that  M. 
Arnaud's  remarks  are  the  result  of  misconceptions. 
I  will  try  therefore  to  deflect  him  from  that  strange 
opinion,  which  he  conceived  a  little  too  hurriedly. 

I  said  in  the  I3th  article  of  my  summary  that  the 
individual  concept  of  each  person  involved  once 
for  all,  all  that  would  ever  happen  to  him.  From  that 
he  draws  this  conclusion  that  all  that  happens  to 
any  person  and  even  to  the  whole  human  race  must 
occur  by  a  necessity  more  than  fatal,  as  though 
concepts  and  previsions  rendered  things  necessary 
and  as  though  a  free  act  could  not  be  included  in 
the  concept  or  perfect  view  which  God  has  of  the 
person  who  performs  it.  And  he  adds  that  per- 
haps I  will  not  find  difficulties  in  the  conclusion 
which  he  draws.  Yet  I  have  expressly  protested  in 
that  same  article  that  I  do  not  admit  such  a  conclu- 
sion. It  must  be  then  either  that  he  doubts  my 
sincerity  for  which  I  have  given  him  no  grounds  or 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  77 

else  he  has  not  sufficiently  examined  that  which  he 
controverts.  I  do  not  complain  as  much  as  it 
appears  I  have  a  right  to,  because  I  remember  that 
he  was  writing  at  a  time  when  an  indisposition  did 
not  permit  him  the  liberty  of  his  whole  mind,  as  the 
letter  itself  witnesses.  And  I  desire  to  have  him 
know  how  much  regard  I  have  for  him. 

He  says:  "If  this  is  true  (that  is  to  say  that  the 
individual  concept  of  each  person  involves  once 
for  all  all  that  will  ever  happen  to  him),  God  has 
not  been  free  to  create  everything  that  has  since 
happened  to  the  human  race,  and  all  that  will  hap- 
pen to  it  for  all  eternity  must  occur  through  a 
necessity  more  than  fatalistic."  (There  is  some  fault 
in  the  copy  but  I  have  felt  able  to  amend  it  as 
above.)  "For  the  individual  concept,  Adam,  has 
involved  that  he  should  have  so  many  children 
and  the  individual  concept  of  each  one  of  these 
children  has  involved  everything  that  they  would 
do  and  all  the  children  that  they  would  have,  and 
so  on.  There  is  therefore  no  more  liberty  in  God 
regarding  all  that,  supposing  that  he  wished  to 
create  Adam,  than  there  is  to  create  a  nature 
incapable  of  thought,  supposing  that  he  wished  to 
create  me." 

To  these  last  words  ought  properly  to  have  been 
added  the  proof  of  the  consequence  but  it  is  quite 
evident  that  they  confuse  necessitatem  ex  hypothesi 
with  absolute  necessity.  A  distinction  has  always 
been  made  between  God's  freedom  to  act  absolutely 
and  his  obligation  to  act  in  virtue  of  certain  resolu- 
tions already  made.  He  hardly  understands  the 
case  who  does  not  take  the  whole  into  considera- 
tion. It  is  little  consonant  with  God's  dignity  to 


78  CORRESPONDENCE. 

conceive  of  him  (with  the  pretext  of  assuring  his 
freedom)  like  certain  Socinians,  as  a  human  being 
who  forms  his  resolutions  according  to  circum- 
stances. These  maintain  that  he  would  be  no 
longer  free  to  create  what  he  found  good  if  his  first 
resolutions  in  regard  to  Adam  or  other  men  already 
involved  a  relationship  to  that  which  concerned 
their  posterity.  Yet  all  agree  that  God  has  regu- 
lated from  all  eternity  the  whole  course  of  the 
universe  without  this  fact  diminishing  his  freedom 
in  any  respect.  It  is  clear  also  that  these  objec- 
tors separate  the  will-acts  of  God  one  from  another 
while  his  acts  are  in  fact  inter-related.  For  we 
must  not  think  of  the  intention  of  God  to  create 
a  certain  man  Adam  as  detached  from  all  the  other 
intentions  which  he  has  in  regard  to  the  children 
of  Adam  and  of  all  the  human  race,  as  though  God 
first  made  the  decree  to  create  Adam  without  any 
relation  to  his  posterity.  This,  in  my  opinion, 
does  away  with  his  freedom  in  creating  Adam's 
posterity  as  seems  best  to  him,  and  is  a  very  strange 
sort  of  reasoning.  We  must  rather  think  that  God, 
choosing  not  an  indeterminate  Adam  but  a  par- 
ticular Adam,  whose  perfect  representation  is  found 
among  the  possible  beings  in  the  Ideas  of  God  and 
who  is  accompanied  by  certain  individual  circum- 
stances and  among  other  predicates  possesses  also 
that  of  having  in  time  a  certain  posterity, — God,  I 
say,  in  choosing  him,  has  already  had  in  mind  his 
posterity  and  chooses  them  both  at  the  same  time. 
I  am  unable  to  understand  how  there  is  any  evil 
in  this  opinion.  If  God  should  act  in  any  other 
way  he  would  not  act  as  God.  I  will  give  an  illus- 
tration. A  wise  prince  in  choosing  a  general  whose 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS  79 

intimates  he  knows,  chooses  at  the  same  time  cer- 
tain colonels  and  captains  whom  he  well  knows  this 
general  will  recommend  and  whom  he  will  not  wish 
to  refuse  to  him  for  certain  prudential  reasons. 
This  fact,  however,  does  not  at  all  destroy  the 
absolute  power  of  the  prince  nor  his  freedom.  The 
same  applies  to  God  even  more  certainly. 

Therefore  to  reason  rightly  we  must  think  of  God 
as  having  a  certain  more  general  and  more  compre- 
hensive intention  which  has  regard  to  the  whole 
order  of  the  universe  because  the  universe  is  a  whole 
which  God  sees  through  and  through  with  a  single 
glance.  This  more  general  intention  embraces 
virtually  the  other  intentions  touching  what  tran- 
spires in  this  universe  and  among  these  is  also  that 
of  creating  a  particular  Adam  who  is  related  to  the 
line  of  his  posterity  which  God  has  already  chosen 
as  such  and  we  may  even  say  that  these  particular 
intentions  differ  from  the  general  intention  only  in 
a  single  respect,  that  is  to  say,  as  the  situation  of 
a  city  regarded  from  a  particular  point  of  view  has 
its  particular  geometrical  plan.  These  various 
intentions  all  express  the  whole  universe  in  the 
same  way  that  each  situation  expresses  the  city. 
In  fact  the  wiser  a  man  is,  the  less  detached  inten- 
tions does  he  have,  and  again  the  more  views  and 
intentions  that  one  has  the  less  comprehensive  and 
inter-related  they  are. 

Each  particular  intention  involves  a  relation  to 
all  the  others,  so  that  they  may  be  concerted  together 
in  the  best  way  possible.  Far  from  finding  in  this 
anything  repellent,  I  think  that  the  contrary  view 
destroys  the  perfection  of  God.  In  my  opinion 
one  must  be  hard  to  please  or  else  prejudiced  when 


8o  CORRESPONDENCE. 

he  finds  opinions  so  innocent  or  rather  so  reason- 
able, worthy  of  exaggerations  so  strange  as  those 
which  were  sent  to  Your  Highness. 

If  what  I  said  be  thought  over  a  little  it  will  be 
found  to  be  evident  ex  terminis:  for  by  the  indi- 
vidual concept,  Adam,  I  mean  of  course  a  perfect 
representation  of  a  particular  Adam  who  has  certain 
individual  characteristics  and  is  thus  distinguished 
from  an  infinity  of  possible  persons  very  similar  to 
him  yet  for  all  that  different  from  him  (as  ellipses 
always  differ  from  the  circle,  however  closely  they 
may  approach  it).  God  has  preferred  him  to  these 
others  because  it  has  pleased  God  to  choose  pre- 
cisely such  an  arrangement  of  the  universe,  and 
everything  which  is  a  consequence  of  this  resolu- 
tion is  necessary  only  by  a  hypothetical  necessity 
and  by  no  means  destroys  the  freedom  of  God  nor 
that  of  the  created  spirits.  There  is  a  possible 
Adam  whose  posterity  is  of  a  certain  sort,  and  an 
infinity  of  other  possible  Adams  whose  posterity 
would  be  otherwise;  now  is  it  not  true  that  these 
possible  Adams  (if  we  may  speak  of  them  thus) 
differ  among  themselves  and  that  God  has  chosen 
only  one  who  is  precisely  ours?  There  are  so  many 
reasons  which  prove  the  impossibility,  not  to  say 
the  absurdity  and  even  the  impiety  of  the  contrary 
view,  that  I  believe  all  men  are  really  of  the  same 
opinion  when  they  think  over  a  little  what  they  are 
saying.  Perhaps  M.  A.  also,  if  he  had  not  been 
prejudiced  against  me  as  he  was  at  first,  would  not 
have  found  my  propositions  so  strange  and  would 
not  have  deduced  from  them  the  consequences 
which  he  did. 

I  sincerely  think  I  have  met  M.  Arnaud's  objec- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  8l 

tion  and  I  am  glad  to  see  that  the  point  which  he 
has  selected  as  the  most  startling,  is  in  my  opinion 
so  little  so.  I  do  not  know,  however,  whether  I 
will  have  the  pleasure  of  bringing  M.  Arnaud  to 
acknowledge  it  also.  Among  the  thousand  advan- 
tages of  great  intellectual  ability  there  is  this  little 
defect,  that  those  who  are  possessed  of  this  great 
intellectual  ability,  having  the  right  to  trust  to  their 
opinions,  are  not  easily  changed.  As  for  myself, 
who  am  not  of  this  stamp,  I  glory  in  acknowledging 
that  I  have  been  taught,  and  I  should  even  find  pleas- 
ure in  being  taught,  provided  I  could  say  it  sincerely 
and  without  flattery. 

In  addition  I  wish  M.  Arnaud  to  know  that  I 
make  no  pretentions  to  the  glory  of  being  an  inno- 
vator, as  he  seems  to  have  understood  my  opinions. 
On  the  contrary  I  usually  find  that  the  most  ancient 
and  the  most  generally  accepted  opinions  are  the 
best.  I  think  that  one  cannot  be  accused  of  being 
an  innovator  when  he  produces  only  certain  new 
truths  without  overturning  well  established  beliefs. 
This  is  what  the  Geometers  are  doing  and  all  those 
who  are  moving  forward.  I  do  not  know  if  it  will  be 
easy  to  indicate  authorized  opinions  to  which  mine 
are  opposed.  That  is  why  what  M.  Arnaud  says 
concerning  the  church  has  nothing  to  do  with  these 
meditations  of  mine,  and  I  hope  that  he  does  not 
wish  to  hold  and  that  he  will  not  be  able  to  prove 
them  to  contain  anything  that  can  be  considered  as 
heretical  in  any  church  whatever.  Yet  if  the  Church 
to  which  he  belongs  is  so  prompt  to  censure,  such 
a  proceeding  should  serve  as  a  notice  to  be  on  one's 
guard.  As  soon  as  a  person  might  wish  to  express, 
some  view  which  would  have  the  slightest  bearing 


82  CORRESPONDENCE. 

upon  Religion  and  which  might  go  a  little  beyond 
what  is  taught  to  children,  he  would  be  in  danger  of 
getting  into  difficulties  or  at  least  of  having  some 
church  father  as  a  sponsor,  which  is  saying  the 
same  things  in  terminis.  Yet  even  that  would  not 
be  perhaps  sufficient  for  complete  safety,  above  all, 
when  one  has  no  means  of  support. 

If  Your  Serene  Highness  were  not  a  Prince  whose 
intelligence  is  as  great  as  is  his  moderation,  I  should 
have  been  on  my  guard  in  speaking  of  these  things. 
To  whom,  however,  do  they  relate  better  than  to 
you,  and  since  you  have  had  the  goodness  to  act  as 
intermediary  in  this  discussion,  can  we  without 
imprudence  have  recourse  to  any  other  arbitrator? 
In  so  far  as  the  concern  is  not  so  much  regarding 
the  truth  of  certain  propositions  as  regarding  their 
consequences  and  their  being  tolerated,  I  do  not 
believe  that  you  will  approve  so  much  vehemence 
over  so  small  a  matter.  It  is  quite  possible,  how- 
ever, that  M.  A.  spoke  in  those  severe  terms  only 
because  he  believed  that  I  would  admit  the  conse- 
quence which  he  had  reason  to  find  so  terrifying  and 
that  he  will  change  his  language  after  my  explana- 
tion. To  this,  his  own  sense  of  justice  will  con- 
tribute as  much  as  the  authority  of  Your  Highness. 
I  am,  with  devotion,  etc. 

IV 
Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

April  12,  1686. 

I  have  received  M.  Arnaud's  verdict  and  I  think 
jt  well  to  disabuse  his  mind  by  the  enclosed  reply 
in  the  form  of  a  letter  to  Your  Highness.  But  I 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  83 

confess  that  I  have  had  much  difficulty  in  suppress- 
ing a  desire  as  much  to  laugh  as  to  express  pity, 
inasmuch  as  the  good  man  seems  really  to  have  lost 
a  part  of  his  mind  and  seems  not  to  have  been  able 
to  keep  from  crying  out  against  everything  as  do 
those  seized  with  melancholy  to  whom  everything 
which  they  see  or  think  of  appears  black.  I  have 
shown  a  good  deal  of  moderation  toward  him  but  I 
have  not  avoided  letting  him  quietly  know  that  he 
is  wrong.  If  he  has  the  kindness  to  rescue  me 
from  the  errors  which  he  attributes  to  me  and  which 
he  thinks  to  have  seen  in  my  writings,  I  wish  that 
he  would  suppress  the  personal  reflections  and  the 
severe  expressions,  which  I  have  feigned  not  to 
notice  out  of  the  respect  which  I  have  for  Your 
Serene  Highness  and  also  because  of  the  respect 
which  I  have  for  the  merits  of  the  good  man. 

Yet  I  am  surprised  at  the  difference  which  there 
is  between  our  pretended  Santons  and  those  persons 
of  the  world  who  pretend  to  no  such  position  and  have 
much  more  the  effect.  Your  Serene  Highness  is  a 
Sovereign  Prince  and  still  you  have  shown  to  me  a 
moderation  which  I  wonder  at,  while  M.  Arnaud  is 
a  famous  theologian  whose  meditations  on  religious 
subjects  ought  to  have  rendered  him  mild  and  char- 
itable, yet  what  he  says  seems  often  haughty,  rough 
and  full  of  severity.  I  am  not  surprised  now  that 
he  has  so  easily  fallen  out  with  Father  Malebranche 
and  others  who  used  to  be  his  fast  friends.  Father 
Malebranche  has  published  writings  which  M. 
Arnaud  treated  extravagantly  almost  as  he  has  done 
in  my  case.  The  world  has  not  always  been  of  his 
opinions.  He  must  take  care,  however,  not  to 
excite  his  bilious  temper.  It  will  deprive  us  of 


84  CORRESPONDENCE. 

all  the  pleasure  and  all  the  satisfaction  which  1 
had  anticipated  in  a  mild  and  reasonable  debate. 

1  believe  he  received  my  paper  when  he  was  in  an 
ill  humor  and  finding  himself  put  to  trouble  by  it, 
he  wanted  to  revenge  himself  by  a  rebuff.  I  know 
that  if  Your  Serene  Highness  had  the  leisure  to  con- 
sider the  objection  which  he  brought  forward,  you 
could  not  refrain  from  laughing  at  seeing  the  slight 
cause  he  had  for  making  such  tragic  exclamations; 
quite  as  one  would  laugh  on  hearing  an  orator  who 
should  say  every  few  minutes,  "O  coelum,  O  terra, 
O  maria  Neptuni." 

I  am  glad  that  there  is  nothing  more  repellent,  or 
more  difficult  in  my  thoughts  than  what  he  objects 
to.  For  according  to  him  if  what  I  say  is  true 
(namely  that  the  individual  concept  or  considera- 
tion of  Adam,  involves  all  that  will  happen  to  him 
and  to  his  posterity),  it  follows  that  God  will  have 
no  liberty  any  longer  with  respect  to  the  human 
race.  He  imagines  therefore  that  God  is  like  a 
human  being  who  forms  his  resolves  in  accordance 
with  circumstances,  while  on  the  contrary,  God, 
foreseeing  and  having  regulated  all  things  from  all 
eternity,  has  chosen  from  the  first  the  entire  sequence 
and  inter-relation  of  the  universe  and  consequently 
not  simply  an  Adam  but  such  an  Adam  in  regard  to 
whom  he  foresaw  that  he  would  do  such  and  such 
things  and  would  have  such  and  such  children,  with- 
out, however,  this  prevision  of  God's,  though 
ordained  from  all  time,  interfering  at  all  with  his 
freedom.  On  this  point  all  theologians,  excepting 
some  Socinians  who  think  of  God  as  a  human  being, 
are  agreed.  And  I  am  surprised  that  the  desire  to 
find  something  repellent  in  my  thoughts,  prejudice 


LEIBNIZ.       ARNAULD.       HKSSEN-RHEINFELS.  85 

against  which  had  engendered  in  his  mind  a  con- 
fused and  ill-directed  idea,  has  led  this  learned  man 
to  speak  against  his  own  knowledge  and  convic- 
tions. For  I  am  not  so  unfair  as  to  imitate  him 
and  to  impute  to  him  the  dangerous  doctrine  of 
those  Socinians  which  destroys  the  sovereign  per- 
fection of  God,  although  he  seems  almost  to  incline 
to  that  doctrine  in  the  heat  of  debate. 

Every  man  who  acts  wisely  considers  all  the  cir- 
cumstances and  bearings  of  the  resolve  which  he 
makes,  and  this  in  accordance  with  the  measure  of 
his  abilities.  And  God,  who  sees  every  thing  per- 
fectly and  with  a  single  glance,  can  he  have  failed 
to  make  his  plans  in  conformity  with  everything 
which  he  saw?  And  can  he  have  chosen  a  particular 
Adam  without  considering  and  having  in  mind  all 
that  has  relations  to  him?  Consequently  it  is  ridic- 
ulous to  say  that  this  free  resolve  on  God's  part 
deprives  him  of  his  liberty.  Otherwise  in  order  to 
be  free  one  must  need  be  ever  undecided.  Such 
are  the  thoughts  which  are  repellent  to  Mr.  Arnaud. 
We  will  see  if  through  their  consequences  he  will 
be  able  to  derive  something  worse  from  them.  Yet 
the  most  important  reflection  which  I  have  made 
in  the  enclosed  is  that  he  himself  some  time  ago 
expressly  wrote  to  Your  Serene  Highness  that  no 
trouble  was  given  to  a  man  who  was  in  their  church 
or  who  wished  to  be  in  it,  for  his  philosophical 
opinions  and  here  is  he  now,  forgetting  this  modera- 
tion, and  losing  control  of  himself  over  a  trifle.  It 
is  therefore  dangerous  to  consort  with  such  people 
and  Your  Serene  Highness  sees  how  many  precau- 
tions one  should  take.  This  was  one  of  the  very 
reasons  why  I  communicated  the  summary  to  M. 


86  CORRESPONDENCE. 

Arnaud,  viz.,  to  probe  a  little  and  to  see  what  his 
behaviour  would  be.  But  tange  monies  et  fumiga- 
bunt  As  soon  as  one  swings  away  the  least  amount 
from  the  positions  of  certain  professors  they  burst 
forth  into  explosions  and  thunders. 

I  am  very  positive  that  the  world  will  not  be  of 
his  opinion  but  it  is  always  well  to  be  on  one's 
guard.  Perhaps,  however,  Your  Highness  will 
have  a  chance  to  let  him  know  that  to  act  in  such 
a  way,  is  to  rebuke  people  unnecessarily,  so  that 
henceforth  he  may  use  a  little  more  moderation. 
If  I  am  not  mistaken  Your  Highness  had  a  corre- 
spondence with  him  about  the  methods  of  restraint 
and  I  should  like  to  learn  the  results  of  it. 

I  may  add  that  milord  has  now  gone  to  Rome  and 
apparently  will  not  return  to  Germany  so  soon  as 
was  thought.  One  of  these  days  I  am  going  to 
Wolfenbiitel  and  will  do  my  best  to  recover  Your 
Highness's  book.  It  is  said  that  M.  Varillas  has 
written  a  History  of  Modern  Heresies. 

Mastrich's  letter  which  Your  Highness  commun- 
icated to  me  regarding  the  conversions  of  Sedan 
seems  quite  reasonable.  M.  Maimburg,  they  say, 
reports  that  St.  Gregory  the  Great  also  approved  of 
this  principle,  namely  that  one  should  not  trouble 
himself  even  if  the  conversion  of  Heretics  was 
feigned,  provided  that  thus  their  children  were 
really  gained  over.  But  it  is  not  permitted  to  kill 
some  persons  in  order  to  gain  others,  although 
Charlemagne  used  almost  exactly  this  method 
against  the  Saxons,  forcing  them  to  accept  Religion 
with  the  sword  at  their  throats.  We  have  now  here 
a  Monsieur  Leti  who  has  brought  us  his  History  of 
Geneva  in  five  volumes  dedicated  to  the  House  of 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  87 

Brunswick.  I  do  not  know  what  relationship  he 
finds  between  the  two.  He  says  quite  good  things 
at  times  and  is  a  good  conversationalist. 

I  am,  etc. 

V 
Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

5/15  April,  1686. 

Your  Serene  Highness  will  have  received  the  let- 
ter which  I  sent  by  the  preceding  post,  to  which  I 
joined,  in  the  form  of  a  letter  to  Your  Highness,  a 
communication  of  which  a  copy  could  be  sent  to 
M.  A.  I  have  since  thought  it  would  be  better  to 
change  those  words  toward  the  end,  beginning 
"Nevertheless,  if  the  church  in  which  he  is  be  so 
prompt  to  censure,  such  a  procedure  ought  to  serve 
as  a  notice,"  etc.,  as  far  as  the  words,  "above  all, 
when  one  has  no  means  of  support,"  lest  M.  A. 
may  take  the  opportunity  from  them  to  enter 
into  controversial  disputes  as  if  the  church 
were  being  attacked,  which  is  not  at  all  the  inten- 
tion. 

In  the  copy  could  be  put  in  their  place,  "least  of 
all  in  the  communion  to  which  M.  A.  belongs, 
where  the  Council  of  Trent  as  well  as  the  Popes 
have  been  very  wisely  satisfied  with  censuring 
opinions  in  which  there  are  points  manifestly 
against  the  faith  and  against  the  customs.  They 
have  not  gone  into  the  philosophic  consequences. 
If  it  were  necessary  to  listen  to  these,  then  in  mat- 
ters of  censure  Thomists  would  pass  for  Calvinists 
according  to  the  Jesuits,  and  the  Jesuits  would  be 
classed  as  Semipelagians  according  to  the  Thomists. 


88  CORRESPONDENCE. 

Both  would  destroy  freedom  according  to  Durandus 
and  Father  Louys  de  Dole,  and  in  general  every 
absurdity  would  pass  for  atheism  because  it  could  be 
shown  to  destroy  the  nature  of  God." 

VI 

Arnauld  to  Leibniz. 

May  13,  1686. 

I  thought  that  I  ought  to  address  myself  to  you 
personally  to  ask  pardon  for  having  given  you  cause 
to  become  angry  against  me,  in  that  I  employed  too 
severe  terms  when  I  indicated  what  I  thought  of  one 
of  your  positions.  But  I  protest  before  God  that 
the  fault  which  I  committed  was  not  at  all  the  result 
of  prejudice  against  you,  for  I  have  never  had  cause 
to  have  of  you  other  than  a  most  favorable  opin- 
ion save  in  the  matter  of  Religion,  in  which  you 
found  yourself  fixed  through  your  birth;  neither  was 
I  in  an  ill  humor  when  I  wrote  the  letter  which  has 
wounded  you,  nothing  being  further  from  my  char- 
acter than  the  evil  disposition  which  it  pleases  many 
people  to  attribute  to  me;  neither  by  a  too  great 
attachment  to  my  own  opinions  was  I  shocked  in  see- 
ing you  hold  contrary  opinions,  for  I  can  assure  you 
that  I  have  meditated  so  little  on  these  kinds  of 
subjects  that  I  am  able  to  say  that  my  opinions  are 
not  at  all  fully  made  up. 

I  beg  you,  sir,  to  believe  nothing  like  that  about 
me  but  to  be  convinced  that  what  caused  my  indis- 
cretion was  simply  that,  having  been  accustomed  to 
write  off-hand  to  His  Highness  because  he  is  so 
good  as  to  readily  excuse  all  my  faults,  I  imagined 
that  I  could  tell  him  frankly  what  I  was  unable  to 
approve  of  in  one  of  your  opinions  because  I  was 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  89 

very  sure  it  would  not  pass  muster  and  if  I  had 
misunderstood  your  meaning  you  would  be  able  to 
correct  me  without  its  going  any  further. 

But  I  hope,  sir,  that  the  Prince  will  be  willing  to 
make  peace  for  me  and  I  may  engage  him  in  this 
by  using  the  words  which  Saint  Augustine  used  on 
a  similar  occasion.  He  had  written  very  harshly 
against  those  who  thought  that  God  could  be  seen 
with  the  physical  eyes,  and  a  Bishop  in  Africa  who 
held  this  opinion,  having  seen  this  letter  which  was 
not  at  all  addressed  to  him,  was  seriously  offended 
by  it.  This  necessitated  Saint  Augustine's  employ- 
ing a  common  friend  to  appease  the  Prelate  and  I 
beg  you  to  imagine  that  I  am  saying  to  the  Prince 
for  your  ears  what  Saint  Augustine  wrote  to  this 
friend,  to  be  said  to  the  Bishop:  Dum  essem  in 
admonendo  sollicitus,  in  corripiendo  nimius  atque 
improvidus  fui.  Hoc  non  defendo  sed  reprehendo:  hoc 
non  excuse,  sed  accuso.  Ignoscatur,  peto ;  recordetur 
nostrum  dilectionem  pristinem  et  obliviscatur  offensionem 
novam.  Faciat  certe  quod  me  non  fecisse  succensuit: 
habeat  lenitatem  in  dandi  venia,  quam  non  habui  in  ilia 
epistola  conscribenda. 

I  was  in  doubt  whether  I  ought  not  to  stop  here 
without  going  again  into  the  question  which  was 
the  occasion  for  our  falling  out,  lest  there  might 
again  escape  me  some  word  which  could  wound 
you.  But  I  fear,  however,  that  that  would  be  not 
to  have  a  sufficiently  good  opinion  of  your  fairness. 
I  will  tell  you,  therefore,  in  a  few  words  the  diffi- 
culties which  I  still  have  with  this  proposition: 
"The  individual  concept  of  each  person  involves, 
once  for  all,  all  that  will  ever  happen  to  him." 

It  seems  to  me  to  follow  from  this  that  the  indi- 


90  CORRESPONDENCE. 

vidual  concept  of  Adam  has  involved  that  he  would 
have  so  many  children  and  the  individual  concept 
of  each  one  of  these  children  involves  all  that  they 
will  do  and  all  the  children  which  they  will  have 
and  so  on.  Whence  I  thought  that  we  could  infer 
that  God  was  free,  in  so  far  as  the  creating  or  not 
creating  of  Adam,  but  supposing  that  he  had  wished 
to  create  him,  all  that  has  since  happened  to  the 
human  race  has  come  and  must  come  by  a  fatalistic 
necessity  or  I  thought  at  least  that  there  was  no 
more  freedom  in  God  regarding  all  that,  supposing 
that  he  had  wished  to  create  Adam,  than  there  was 
not  to  create  a  being  capable  of  thinking,  suppos- 
ing he  had  wished  to  create  me. 

It  does  not  appear  to  me,  Monsieur,  that,  in 
speaking  thus,  I  have  confused  necessitate™,  ex 
hypothesi  and  absolute  necessity,  for  I  was  all  the 
time  speaking  only  against  the  necessity  ex 
hypothesi;  what  I  find  strange  is,  that  all  human 
events  should  be  quite  as  necessary  by  a  necessity  ex 
hypothesi  after  this  first  supposition  that  God 
wished  to  create  Adam,  as  it  is  necessary  by  the 
same  necessity  for  there  to  be  in  the  world  a  nature 
capable  of  thinking  simply  because  he  has  wished 
to  create  me. 

You  say  in  this  connection  various  things  about 
God  which  do  not  seem  to  me  sufficient  to  solve  my 
difficulty. 

1.  "That   a   distinction   has    always    been   made 
between  what  God  is  free  to  do  absolutely  and  what 
he  is  obliged  to  do  by  virtue  of  certain  resolutions 
already  made."     This  position  is  valid, 

2.  "That  it  is  little  consonant  with  the  dignity 
of  God  to  conceive  of  him  (under  the  pretext  of 


LEIBNIZ.       ARNAULD.        HESSEN-RHEINFELS.  9! 

safeguarding  his  freedom)  in  the  way  that  the 
Socinians  do,  as  a  man  who  forms  his  resolutions 
according  to  the  circumstances."  Such  an  opinion 
is  very  foolish,  I  grant  you. 

3.  "That  the  purposes  of  God,  which  are  all  inter- 
related must  not  be  isolated.  Therefore,  the  purpose 
of  God  to  create  a  particular  Adam  must  not  be 
looked  at  detached  from  all  the  others  which  he  has 
regarding  the  children  of  Adam  and  of  the  whole 
human  race."  To  this  also  I  agree,  but  I  cannot 
yet  see  how  these  can  serve  to  solve  my  difficulty. 

For  i.  I  confess,  in  good  faith,  not  to  have  under- 
stood that,  by  the  individual  concept  of  each  person 
(for  example  of  Adam),  which  you  say  involves, 
once  for  all,  all  that  will  ever  happen  to  him,  you 
meant  this  person  in  so  far  as  he  is  in  the  divine 
understanding  instead  of  simply  what  he  is  in  himself. 
For  it  seems  to  me  that  it  is  not  customary  to  con- 
sider the  specific  concept  of  a  sphere  in  relation  to 
that  which  is  its  representation  in  the  divine  under- 
standing but  in  relation  to  what  it  is  in  itself.  I 
thought  it  was  thus  with  the  individual  concept  of 
~ach  person  or  of  everything. 

2.  It  is  enough,  however,  for  me  to  know  what  you 
intend,  so  that  I  can  conform  to  it,  and  inquire  if 
that  overcomes  all  the  difficulty  which  I  mentioned 
above.  It  does  not  seem  to  me  that  it  does. 

I  agree  that  the  knowledge  which  God  had  of 
Adam  when  he  resolved  to  create  him  involved 
what  happened  to  him  and  what  has  happened,  or 
will  happen,  to  his  posterity;  and  therefore  if  we 
understand  in  this  sense  the  individual  concept, 
Adam,  what  you  say  about  it  is  very  true. 

I  grant  also  that  the  purpose  which  he  had   in 


92  CORRESPONDENCE. 

creating  Adam  was  not  detached  from  that  which 
he  had  regarding  what  would  happen  to  him  and  in 
regard  to  all  his  posterity. 

But  it  seems  to  me,  that  after  all  this  there  still 
remains  the  question  (and  this  is  where  my  diffi- 
culty lies)  whether  the  relationship  between  those 
objects  (I  mean  Adam  on  the  one  hand  and  what 
will  happen  to  him  and  to  his  posterity  on  the 
other),  is  such  through  itself,  independently  of  all 
the  free  decrees  of  God;  or,  whether  it  has  been 
dependent.  That  is  to  say,  whether  it  is  only  in 
consequence  of  the  free  decrees  by  which  God  has 
foreordained  all  that  will  happen  to  Adam  and  to 
his  posterity  that  God  has  known  all  that  will  happen 
to  Adam  and  to  his  posterity;  or  whether  there  is, 
independent  of  these  decrees,  between  Adam  on 
the  one  hand,  and  what  has  happened  and  will  hap- 
pen to  him  and  his  posterity  on  the  other,  an  intrin- 
sic and  necessary  connection.  Unless  you  mean  the 
latter  I  do  not  see  how  it  can  be  true  when  you  say, 
"that  the  individual  concept  of  each  person  involves 
once  for  all,  all  that  which  will  ever  happen  to  him," 
even  if  we  understand  this  concept  in  its  relation  to 
God. 

It  seems,  moreover,  that  it  is  this  latter  which 
you  do  not  accept.  For  I  believe  you  to  suppose 
that,  according  to  our  way  of  conceiving,  possible 
things  are  possible  before  any  free  decree  of  God, 
whence  it  follows  that  what  is  involved  in  the  con- 
cept of  possible  things  is  involved  independently  of 
all  God's  free  decrees.  Now  you  say  "that  God 
has  found  among  possible  things  a  possible  Adam, 
accompanied  by  certain  individual  circumstances, 
who,  among  other  predicates,  possesses  also  that  of 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  93 

having  in  time  a  certain  posterity."  There  is, 
therefore,  according  to  you  a  connection  intrinsic, 
so  to  speak,  and  independent  of  all  the  free  decrees  of 
God;  a  connection  between  this  possible  Adam  and 
all  the  separate  persons  of  his  posterity  and  not  the 
persons  alone,  but  in  general  all  that  must  happen 
to  them.  It  is  this,  Monsieur,  I  speak  plainly,  that 
is  incomprehensible  to  me.  For  your  meaning 
seems  to  be  that  the  possible  Adam  whom  God  has 
chosen  preferably  to  other  possible  Adams,  had  a 
connection  with  the  very  same  posterity  as  the 
created  Adam.  In  either  case  it  is,  as  far  as  I  can 
judge,  the  same  Adam  considered  now  as  possible 
and  now  as  created.  If  this  is  your  meaning  then 
here  is  my  difficulty. 

How  many  men  there  are  who  have  come  into  the 
world  only  through  the  perfectly  free  decrees  of 
God,  such  as  Isaac,  Samson,  Samuel  and  many 
others!  Now  the  fact  that  God  has  known  them 
conjointly  with  Adam  is  not  owing  to  their  having 
been  involved  independently  of  the  decrees  of  God 
in  the  individual  concept  of  the  possible  Adam.  It 
is,  therefore,  not  true  that  all  the  individual  person- 
ages of  the  posterity  of  Adam  have  been  involved  in 
the  individual  concept  of  the  possible  Adam  since 
they  would  then  have  been  thus  involved  inde- 
pendently of  God's  decress. 

The  same  can  be  said  of  an  infinite  number  of 
human  events  which  have  occurred  by  the  express 
and  particular  commands  of  God,  for  instance,  the 
Jewish  and  Christian  Religions,  and,  above  all,  the 
Incarnation  of  the  Word  of  God.  I  do  not  see  how 
it  can  be  said  that  all  these  are  involved  in  the 
individual  concept  of  the  possible  Adam.  What- 


94  CORRESPONDENCE. 

ever  is  considered  as  possible  must  have  all  that  is 
conceived  of  under  this  idea  of  possibility  independ- 
ently of  the  Divine  decrees. 

Moreover,  Monsieur,  I  do  not  see  how,  in  taking 
Adam  as  an  example  of  a  unitary  nature,  several 
possible  Adams  can  be  thought  of.  It  is  as  though 
I  should  conceive  of  several  possible  me's;  a  thing 
which  is  certainly  inconceivable.  For  I  am  not 
able  to  think  of  myself  without  considering  myself 
as  a  unitary  nature,  a  nature  so  completely  distin- 
guished from  every  other  existent  or  possible  being 
that  I  am  as  little  able  to  conceive  of  several  me's 
as  to  think  of  a  circle  all  of  whose  diameters  are  not 
equal.  The  reason  is  that  these  various  me's  are 
different,  one  from  the  other,  else  there  would  not 
be  several  of  them.  There  would  have  to  be,  there- 
fore, one  of  these  me's  which  would  not  be  me,  an 
evident  contradiction. 

Permit  me,  therefore,  Monsieur,  to  transfer  to  this 
me  what  you  say  concerning  Adam  and  you  may 
judge  for  yourself  if  it  will  hold.  Among  possible 
beings  God  has  found  in  his  ideas  several 
me's,  of  which  one  has  for  its  predicates,  to  have 
several  children  and  to  be  a  physician,  and  another 
to  live  a  life  of  celibacy  and  to  be  a  Theologian. 
God,  having  decided  to  create  the  latter,  or  the 
present  me,  includes  in  its  individual  concept  the 
living  a  life  of  celibacy  and  the  being  a  Theologian 
while  the  former  would  have  involved  in  its  indi- 
vidual concept  being  married  and  being  a  physician. 
Is  it  not  clear  that  there  would  be  no  sense  in  such 
statements,  because,  since  my  present  me  is  neces- 
sarily of  a  certain  individual  nature,  which  is  the 
same  thing  as  having  a  certain  individual  concept, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  95 

it  will  be  as  impossible  to  conceive  of  contradictory 
predicates  in  the  individual  concept  me,  as  to  con- 
ceive of  a  me  different  from  me?  Therefore  we 
must  conclude,  it  seems  to  me,  that  since  it  is 
impossible  for  me  not  to  always  remain  myself 
whether  I  marry  or  whether  I  live  a  life  of  celibacy, 
the  individual  concept  of  my  me  has  involved 
neither  the  one  nor  the  other  of  those  two  states. 
Just  as  we  might  say  that  this  block  of  marble  is  the 
same  whether  it  be  in  repose  or  in  a  state  of  move- 
ment and  therefore  neither  movement  nor  repose 
are  involved  in  its  individual  concept.  This  is  why 
Monsieur,  it  seems  to  me,  that  I  ought  to  regard  as 
involved  in  my  individual  concept  only  what  is  of 
such  a  nature  that  I  would  no  longer  be  myself  if  it 
were  not  in  me,  while,  on  the  other  hand,  every- 
thing which  is  of  such  a  nature  that  it  might  either 
happen  to  me  or  not  happen  to  me  without  my 
ceasing  to  be  myself,  should  not  be  considered  as 
involved  in  my  individual  concept;  (although,  by 
the  ordinance  of  God's  providence,  which  never 
changes  the  nature  of  things,  it  could  never  happen 
that  that  should  be  in  me).  This  is  my  thought, 
which,  1  believe,  conforms  wholly  to  what  has  always 
been  held  by  all  the  philospohers  in  the  world. 

That  which  confirms  me  in  this  position  is  the 
difficulty  I  experience  in  believing  it  to  be  good 
philosophy,  to  seek  in  God's  way  of  knowing  things, 
what  we  ought  to  think  out,  either  from  their  specific 
concepts  or  from  their  individual  concepts.  The 
divine  understanding  is  the  measure  of  the  truth  of 
things,  quoad  se,  (as  far  as  they  are  concerned,)  but 
it  does  not  appear  to  me  that,  inasmuch  as  we  are  in 
this  life,  it  can  be  the  measure  for  us,  quoad  nos. 


9<5  CORRESPONDENCE. 

For  what  do  we  know  at  present  of  God's  knowl- 
edge? We  know  that  he  knows  all  things  and  that 
he  knows  them  all  by  a  single  and  very  simple  act, 
which  is  his  essence.  When  I  say  that  we  know  it 
I  mean  that  we  are  sure  that  this  must  be  so.  But 
do  we  understand  it?  And  ought  we  not  to  recog- 
nize that  however  sure  we  may  be  that  it  is  so,  it  is 
impossible  for  us  to  conceive  how  it  can  be? 
Further,  are  we  able  to  conceive  that,  although  the 
knowledge  of  God  is  his  very  essence,  wholly  neces- 
sary and  immutable,  he  has,  nevertheless,  knowledge 
of  an  infinity  of  things  which  he  might  not  have  had 
because  these  things  might  not  have  been?  It  is 
the  same  in  the  case  of  his  will  which  is  also  his 
very  essence  where  there  is  nothing  except  what  is 
necessary;  and  still  he  wills  and  has  willed,  from  all 
eternity,  things  which  he  would  have  been  able  not 
to  will.  I  find  therefore  a  great  deal  of  uncertainty 
in  the  manner  in  which  we  usually  represent  to  our- 
selves that  God  acts.  We  imagine  that  before  pur- 
posing to  create  the  world  he  looked  over  an 
infinity  of  possible  things,  some  of  which  he  chose 
and  rejected  the  others — many  possible  Adams, 
each  one  with  a  great  sequence  of  persons  and 
events  between  whom  there  was  an  intrinsic  con- 
nection. And  we  think  that  the  connection  of  all 
these  other  things  with  the  one  of  the  possible 
Adams  is  exactly  like  that  which  we  know  has  been 
between  the  created  Adam  and  all  his  posterity. 
This  makes  us  think  that  it  was  that  one  of  all  the 
possible  Adams  which  God  chose  and  that  he  did 
not  at  all  wish  any  of  the  others.  Without  however 
stopping  over  that  which  I  have  already  said, 
namely,  that  taking  Adam  for  an  example  of  a 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  97 

unitary  nature  it  is  as  little  possible  to  conceive  of 
several  Adams  as  to  conceive  of  several  me's,  I 
acknowledge  in  good  faith  that  I  have  no  idea  of 
substances  purely  possible,  that  is  to  say,  which 
God  will  never  create.  I  am  inclined  to  think  that 
these  are  chimeras  which  we  construct  and  that 
whatever  we  call  possible  substances,  pure  possi- 
bilities are  nothing  else  than  the  omnipotence  of 
God  who,  being  a  pure  act,  does  not  allow  of  there 
being  a  possibility  in  him.  Possibilities,  however, 
may  be  conceived  of  in  the  natures  which  he  has 
created,  for,  not  being  of  the  same  essence  through- 
out, they  are  necessarily  composites  of  power  and 
action.  I  can  therefore  think  of  them  as  possi- 
bilities. I  can  also  do  the  same  with  an  infinity  of 
modifications  which  are  within  the  power  of  these 
created  natures,  such  as  are  the  thoughts  of  intelli- 
gent beings,  and  the  forms  of  extended  substance. 
But  I  am  very  much  mistaken  if  there  is  any  one 
who  will  venture  to  say  that  he  has  an  idea  of  a 
possible  substance  as  pure  possibility.  As  for 
myself,  I  am  convinced  that,  although  there  is  so 
much  talk  of  these  substances  which  are  pure  possi- 
bilities, they  are,  nevertheless,  always  conceived  of 
only  under  the  idea  of  some  one  of  those  which  God 
has  actually  created.  We  seem  to  me,  therefore, 
able  to  say  that  outside  of  the  things  which  God  has 
created,  or  must  create,  there  is  no  mere  negative 
possibility  but  only  an  active  and  infinite  power. 

However  that  may  be,  all  that  I  wish  to  conclude 
from  this  obscurity  and  from  the  difficulty  of  know- 
ing the  way  that  things  are   in  the  knowledge  of 
God  and  of  knowing  what  is  the  nature  of  the  con-  • 
nection  which    they  have    among  themselves    and 


98  CORRESPONDENCE. 

whether  it  is  intrinsic  or,  so  to  speak,  extrinsic- 
all  that  I  wish  to  conclude,  I  say,  from  this,  is  that 
it  is  not  through  God,  who  with  respect  to  us, 
dwells  in  inaccessible  light,  that  we  should  try  to 
find  the  true  concepts  either  specific  or  individual  of 
the  things  we  know;  but  it  is  in  the  ideas  about 
them  which  we  find  in  ourselves. 

Now  I  find  in  myself  the  concept  of  an  individual 
nature  since  I  find  there  the  concept  me.  I  have,  there- 
fore, only  to  consult  it  in  order  to  know  what  is 
involved  in  this  individual  concept,  just  as  I  have 
only  to  consult  the  specific  concept  of  a  sphere  to 
know  what  is  involved  there.  Now  I  have  no  other 
rule  in  this  respect  except  to  consider  whether  the 
properties  are  of  such  a  character  that  a  sphere  would 
no  longer  be  a  sphere  if  it  did  not  have  them;  such, 
for  instance,  as  having  all  the  points  of  its  circum- 
ference equally  distant  from  the  center.  Or  to  con- 
sider whether  the  properties  do  not  affect  its  being 
a  sphere,  as  for  instance,  having  a  diameter  of  only 
one  foot  while  another  sphere  might  have  ten, 
another  a  hundred.  I  judge  by  this  that  the  former 
is  involved  in  the  specific  concept  of  a  sphere 
while  the  latter,  which  was  the  having  a  greater  or 
smaller  diameter,  is  not  at  all  involved  in  it. 

The  same  principle  I  apply  to  the  individual  con- 
cept me.  I  am  certain,  that,  inasmuch  as  I  think,  I 
am  myself.  But  I  am  able  to  think  that  I  will 
make  a  certain  journey  or  that  I  will  not,  being 
perfectly  assured  that  neither  the  one  nor  the 
other  will  prevent  me  from  being  myself.  I  main- 
tain very  decidedly  that  neither  the  one  nor  the 
other  is  involved  in  the  individual  concept  me. 
"God  however  has  foreseen,"  it  will  be  said, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  99 

"that  you  will  make  this  journey."  Granted.  "It 
is  therefore  indubitable  that  you  will  make  it." 
I  grant  that  also.  But  does  that  alter  anything 
in  the  certitude  which  I  have  that  whether  I  make 
it  or  do  not  make  it  I  shall  always  be  myself?  I 
must,  therefore,  conclude  that  neither  the  one  nor 
the  other  enters  into  my  me,  that  is  to  say,  into  my 
individual  concept.  It  is  here  it  seems  to  me  that 
we  must  remain  without  having  recourse  to  God's 
knowledge,  in  order  to  find  out  what  the  individual 
concept  of  each  thing  involves. 

This,  Monsieur,  is  what  has  come  into  my  mind 
regarding  the  proposition  which  troubled  me  and 
regarding  the  explanation  which  you  have  given. 
I  do  not  know  if  I  have  wholly  grasped  your 
thought  but  such  has  been  at  least  my  intention. 
The  subject  is  so  abstract  that  a  mistake  is  very 
easy.  I  should,  however,  be  very  sorry  if  you  had 
of  me  as  poor  an  opinion  as  those  who  represent  me 
as  a  hot-headed  writer  who  refutes  others  only  in 
calumniating  them  and  in  purposely  misrepresenting 
their  opinions.  This  is  most  assuredly  not  my 
character.  At  times  I  may  express  my  thoughts 
too  frankly.  At  times  also  I  may  fail  to  grasp  the 
thoughts  of  others  (for  I  certainly  do  not  consider 
myself  infallible,  and  such  one  would  have  to  be  in 
order  never  to  be  mistaken),  but  even  if  this  should 
be  through  self-confidence,  never  would  it  be  that  I 
misstated  them  purposely;  for  I  find  nothing  to  be 
so  low  as  the  using  of  chicanery  and  artifice  in 
differences  which  may  arise  regarding  matters  of 
doctrine.  This  even  if  it  should  be  with  persons 
whom  we  have  no  reason  otherwise  to  love,  and 
still  more  if  the  difference  is  between  friends.  I 


100  CORRESPONDENCE. 

believe,  Monsieur,  that  you  wish  indeed  that  I 
place  you  in  this  latter  class.  I  can  not  doubt  that 
you  do  me  the  honor  to  love  me.  You  have  given 
me  too  many  marks  of  it.  And,  in  my  behalf,  I 
protest  that  the  very  fault  for  which  I  beg  you  once 
more  to  pardon  me,  was  only  the  result  of  the 
affection  which  God  has  given  me  for  you  and  of  a 
zeal  for  your  salvation,  a  zeal  which  has  been  by  no 
means  moderate.  I  am,  etc., 

VII 

Arnauld  to  Count  Ernst  von  Hessen-Rheinfels. 

May  13,  1686. 

I  am  very  sorry,  Monseigneur,  to  have  given  to 
Mr.  Leibniz  cause  to  become  so  angry  at  me.  If  I 
had  foreseen  it,  I  should  have  been  on  my  guard 
against  saying  so  frankly  what  I  thought  of  one  of 
his  metaphysical  propositions.  But  I  ought  to  have 
foreseen  it  and  I  did  wrong  in  employing  such 
severe  terms,  not  against  him  personally  but  against 
his  position.  Therefore,  I  have  felt  myself  com- 
pelled to  beg  his  pardon  for  it  and  I  have  done  it 
very  sincerely  in  the  letter  which  I  have  written  him 
and  am  sending  open  to  Your  Highness.  It  is  also 
from  my  heart  that  I  pray  you  to  make  peace  for 
me  and  to  reconcile  me  with  a  former  friend  of 
whom  I  should  be  very  sorry  to  have  made  an 
enemy  by  my  imprudence. 

I  shall  be  very  glad,  however,  if  the  matter  rests 
there  and  if  I  shall  not  be  obliged  to  tell  him  what 
I  think  of  his  positions,  because  I  am  so  over- 
whelmed with  so  many  other  occupations  that  I 
should  have  difficulty  in  convincing  him  and  these 


LEIBNIZ.       ARNAULD.       HESSEN-RHKINFELS.          IOI 

abstract  subjects  require  a  great  deal  of  application 
which  I  can  not  devote  to  them  on  account  of  the 
time  which  it  consumes. 

I  do  not  know  but  that  I  have  forgotten  to  send 
you  an  addition  to  the  Apology  for  the  Catholics. 
I  fear  lest  I  may  have,  because  Your  Highness  has 
not  mentioned  it  to  me.  I  am  accordingly  sending 
it  to  you  to-day  with  two  Memoirs.  The  Bishop 
of  Namur,  whom  the  Internuncio  has  appointed 
judge,  has  had  difficulty  in  deciding  to  accept  this 
post,  so  great  is  the  fear  of  the  Jesuits.  But  if  their 
power  is  so  great  that  justice  can  not  be  obtained 
against  them  in  this  world,  they  have  reason  to  fear 
that  God  will  punish  them  with  so  much  the  more 
severity  in  the  next.  It  is  a  terrible  history  and 
a  long  one,  that  of  this  Canon,  whose  wickedness 
apparently  would  be  unpunished  if  he  had  not  ren- 
dered himself  odious  by  his  conspiracies  and  his 
cabals. 

This  Lutheran  minister  of  whom  Your  Highness 
speaks  must  have  good  qualities,  but  it  is  some- 
thing incomprehensible  and  marking  an  extremely 
blind  prejudice  that  he  can  regard  Luther  as  a  man 
destined  by  God  for  the  Reformation  of  the  Chris- 
tian religion.  He  must  have  a  very  low  idea  of  true 
piety  to  find  it  in  a  man  like  him,  imprudent  in  his 
speech  and  so  gluttonous  in  his  manner  of  living.  I 
am  not  surprised  at  what  this  minister  has  said  to 
you  against  those  who  are  called  Jansenists,  since 
Luther  at  first  put  forward  extreme  propositions 
against  the  co-operation  of  grace  and  against  the 
freedom  of  will  so  far  as  to  give  to  one  of  his 
books  the  title  De  servo  arbitrio,  Necessitated  Will. 
Melancthon,  some  time  after,  mitigated  these  propo- 


102  CORRESPONDENCE. 

sitions  a  great  deal  and  since  then  the  Lutherans 
have  gone  over  to  the  opposite  extreme  so  that  the 
Arminians  have  nothing  stronger  to  oppose  to  the 
Gummarists  than  the  doctrines  of  the  Lutheran 
Church.  There  is  no  cause  then  for  astonishment 
that  the  Lutherans  of  to-day,  who  occupy  the  same 
positions  as  the  Arminians,  are  opposed  to  the  dis- 
ciples of  Saint  Augustine.  For  the  Arminians  are 
more  sincere  than  are  the  Jesuits.  They  grant  that 
Saint  Augustine  is  opposed  to  them  in  the  opinions 
which  they  have  in  common  with  the  Jesuits  but 
they  do  not  think  themselves  obliged  to  follow  him. 

What  Father  Jobert  is  requiring  from  new  con- 
verts gives  grounds  for  hope  that  those  who  are  con- 
verts only  in  name  may  return,  little  by  little, 
provided  that  instruction  is  given  them,  that  they 
are  edified  by  good  examples,  and  that  the  curacies 
are  filled  with  good  men.  But  it  woud  be  spoiling 
everything  to  take  from  them  the  vernacular  trans- 
lations of  what  is  said  at  Mass.  It  is  only  such 
leniency  that  can  cure  them  from  the  aversion  that 
has  been  given  to  them  regarding  it.  Yet  we  have 
not  yet  been  informed  of  what  has  been  the  outcome 
of  the  storm  aroused  against  the  Annte  Chrttienne, 
about  which  I  wrote  to  Your  Highness  some  time 
ago. 

A  gentleman  named  Mr.  Cicati,  who  is  in  charge 
of  the  Academy  at  Brussels  and  who  says  he  is  well- 
known  by  Your  Highness  because  he  had  the  honor 
to  teach  the  Princes,  Your  sons,  to  ride  on  horse- 
back, is  acquainted  with  a  German,  a  very  honest 
man,  who  knows  French  very  well  and  is  a  good 
lawyer,  even  having  had  a  charge  as  councillor,  and 
who  has  already  been  employed  to  take  charge  of 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS.          103 

young  Seigneurs.  Mr.  Cicati  thinks  that  he  would 
be  a  very  available  man  for  Your  grandsons,  above 
all,  when  they  make  their  journey  in  France  and 
that  meanwhile  he  could  render  other  services  to 
Your  Highness.  I  thought  it  couldn't  do  any  harm 
to  give  you  this  information.  It  binds  you  to 
nothing  and  may  be  of  service  to  you  if  you  think 
it  best  to  have  somebody  with  the  young  Princes— 
someone  who  shall  leave  them  neither  day  nor  night. 
Not  knowing  the  characteristics  of  Mr.  Leibniz,  I 
beg  Your  Highness  to  have  the  above  forwarded 
along  with  the  letter  which  I  have  written  him. 

VIII 

Remarks  upon  Mr.  Arnaud' s  letter  in  regard  to  my 
statement  that  the  individual  concept  of  each  per- 
son involves,  once  for  all,  all  that  will  ever  hap- 
pen to  him: 

May,  1686. 

"I  thought,"  says  Mr.  Arnaud,  "that  we  might 
infer  that  God  was  free  either  to  create  or  not  to 
create  Adam,  but  supposing  that  he  wished  to  create 
him,  all  that  has  since  happened  to  the  human  race 
was,  or  all  which  will  happen  is  by  a  fatalistic 
necessity,  or  we  might  infer  at  least  that  there  was 
no  more  liberty  in  God,  supposing  that  he  once 
wished  to  create  Adam,  than  there  was  of  not 
creating  a  nature  capable  of  thought  in  case  he 
wished  to  create  me."  I  replied  at  first  that  a 
distinction  must  be  made  between  absolute  and 
hypothetical  necessity.  To  this  Mr.  Arnaud  replies 
here  that  he  is  speaking  only  of  necessity  ex 
hypothesi.  After  this  declaration  the  argumenta- 
tion takes  a  different  phase.  The  words  "fatal 


104  CORRESPONDENCE. 

necessity"  which  he  used  and  which  are  ordinarily 
understood  as  an  absolute  necessity  obliged  me  to 
make  this  distinction,  which,  however,  is  now 
uncalled  for,  inasmuch  as  M.  Arnaud  does  not  insist 
upon  the  fatalistic  necessity.  He  uses  alternative 
phrases;  "by  a  fatalistic  necessity  or  at  least,  etc." 

It  would  be  useless  to  dispute  in  regard  to  the 
word.  In  regard  to  the  matter,  however,  M.  Arnaud 
still  finds  it  strange  for  me  to  maintain  "that  all 
human  events  occur  by  necessity  ex  hypothesi  after 
this  single  presupposition  that  God  wished  to  create 
Adam."  To  which  I  have  two  replies  to  give.  The 
one  is,  that  my  supposition  is  not  merely  that  God 
wished  to  create  an  Adam  whose  concept  was  vague 
and  incomplete  but  that  God  wished  to  create  a  par- 
ticular Adam  sufficiently  determined  as  an  indi- 
vidual. This  complete  individual  concept,  in  my 
opinion,  involves  the  relation  to  the  whole  sequence 
of  things — a  position  which  ought  to  appear  so  much 
the  more  reasonable,  because  M.  Arnaud  grants  here 
the  inter-connection  among  the  resolutions  of  God, 
that  is  to  say,  that  God,  having  resolved  to  create  a 
certain  Adam,  takes  into  consideration  all  the  reso- 
lutions which  he  will  form  concerning  the  whole 
sequence  of  the  universe;  almost  in  the  same  way  that 
a  wise  man  who  forms  a  resolution  in  regard  to  one 
part  of  his  plan,  has  the  whole  plan  in  view  and  will 
make  resolutions  better  in  proportion  as  he  is  able 
to  plan  for  all  the  parts  at  the  same  time. 

The  other  reply  is  that  the  sequence,  in  virtue  of 
which  events  follow  from  the  hypothesis,  is  indeed 
always  certain,  but  that  it  is  not  always  necessary 
by  a  metaphysical  necessity,  as  is  that  instance 
which  is  found  in  M.  Arnaud's  example:  that  God, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         105 

resolving  to  create  me,  could  not  avoid  creating  a 
nature  capable  of  thought.  The  sequence  is  often 
only  physical  and  presupposes  certain  free  decrees 
of  God,  as,  for  instance,  do  consequences  which 
depend  on  the  laws  of  motion  or  which  depend  upon 
the  following  principle  of  morality — namely,  that 
every  mind  will  pursue  that  which  appears  to  it  the 
best.  It  is  true  that  when  the  supposition  of  the 
decrees  which  produce  the  consequence  is  added  to 
the  first  supposition  which  constituted  the  antece- 
dent, namely,  God's  resolution  to  create  Adam — it 
is  true,  I  say,  that  if  all  these  suppositions  or  reso- 
lutions are  regarded  as  a  single  antecedent,  then  the 
consequence  follows. 

As  I  have  already  touched  upon  these  two  replies 
somewhat  in  my  letter  sent  to  the  Count,  M.  Arnaud 
brings  forward  answers  to  them  here  which  must  be 
considered.  He  acknowledges  in  good  faith  that  he 
understood  my  opinion  as  if  all  the  events  happen- 
ing to  an  individual  were  deducible  from  his  indi- 
vidual concept  in  the  same  manner  and  with  the 
same  necessity  as  the  properties  of  the  sphere  may 
be  deduced  from  its  specific  concept  or  definition, 
and  as  though  I  had  considered  the  concept  of  the 
individual  in  itself,  without  regard  to  the  manner  in 
which  it  is  present  in  the  understanding  or  will  of 
God.  "For,"  he  says,  "it  seems  to  me  that  it  is 
not  customary  to  consider  the  specific  concept  of  a 
sphere  in  relation  to  its  representation  in  the  divine 
understanding  but  in  relation  to  what  it  is  in  itself, 
and  I  thought  that  it  was  thus  with  the  individual 
concept  of  each  person." 

But,  he  adds,  that  now,  since  he  knows  what  my 
thought  is,  it  is  enough  for  him  to  conform  to  it  in 


106  CORRESPONDENCE. 

inquiring  if  it  overcomes  all  the  difficulties.      Of 
this,  he  is  still  doubtful. 

I  see  that  M.  Arnaud  has  not  remembered,  or  at 
least,  has  not  adhered,  to  the  position  of  the 
Cartesians  who  maintain  that  God,  by  his  will,  estab- 
lishes the  eternal  truths  such  as  are  those  regarding 
the  properties  of  the  sphere.  But,  as  I  share  their 
opinion  no  more  than  does  M.  Arnaud,  I  will  simply 
say  why  I  believe  that  we  must  philosophize  differ- 
ently in  the  case  of  an  individual  substance  from  our 
way  of  philosophizing  in  the  case  of  a  specific  con- 
cept of  the  sphere.  It  is  because  the  concept  of 
space  relations  involves  only  eternal  or  necessary 
truths  but  the  concept  of  an  individual  involves  sub 
ratione  possibilitatis  that  which  is  in  fact  or  which 
has  relation  to  the  existence  of  things  and  to  time, 
and  consequently  it  depends  upon  certain  free 
decrees  of  God  considered  as  possible.  Because 
the  truths  of  fact  or  of  existence  depend  upon  the 
decrees  of  God.  Furthermore,  the  concept  of  the 
sphere  in  general  is  incomplete  or  abstract,  that  is 
to  say  we  consider  only  the  essence  of  the  sphere  in 
general  or  theoretically  without  regard  to  the  par- 
ticular circumstances,  and  consequently  the  concept 
does  not  involve  that  which  is  required  for  the 
existence  of  a  certain  sphere.  The  concept  of  the 
sphere  which  Archimedes  had  put  upon  his  tomb  is 
complete  and  should  involve  all  that  pertains  to  the 
subject  of  this  thing.  That  is  why  in  individual  or 
practical  considerations,  where  singulars  are  dealt 
with,  in  addition  to  the  form  of  the  sphere  there 
enters  the  material  of  which  it  is  made,  the  time, 
the  place,  and  the  other  circumstances  which,  by  a 
continual  network,  would  finally  involve  the  whole 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          107 

sequence  of  the  universe,  provided  we  were  able  to 
follow  out  all  that  these  concepts  involve.  For  the 
concept  of  this  bit  of  matter  out  of  which  this 
sphere  is  made,  involves  all  the  changes  which  it 
has  undergone  and  which  it  will  some  day  undergo. 

In  my  opinion  each  individual  substance  always 
contains  the  traces  of  what  has  ever  happened  to  it 
and  marks  of  that  which  will  ever  happen  to  it. 
What  I  have  just  said,  however,  may  suffice  to 
justify  my  line  of  thought. 

Now,  M.  Arnaud  declares  that  in  taking  the  indi- 
vidual concept  of  a  person  in  relation  to  the  knowl- 
edge which  God  had  of  it  when  he  resolved  to  create 
it,  what  I  have  said  regarding  this  concept  is  very 
true,  and  he  grants  also  that  the  will  to  create  Adam 
was  not  at  all  detached  from  God's  will  in  regard  to 
whatever  has  happened  both  to  him  and  to  his  pos- 
terity. He  now  asks  if  the  connection  between 
Adam  and  the  events  occurring  to  his  posterity  is 
dependent  or  independent  of  the  free  decrees  of 
God.  "That  is  to  say,"  as  he  explains,  "whether  it 
is  only  in  consequence  of  the  free  decrees  by  which 
God  has  ordained  all  that  will  happen  to  Adam  and 
to  his  posterity  that  God  has  known  what  will  hap- 
pen to  them,  or  whether,  independently  of  these 
decrees  there  is  between  Adam  and  the  events 
aforesaid,  an  intrinsic  and  necessary  connection." 

He  does  not  doubt  that  I  would  take  the  second 
alternative  and,  in  fact,  I  am  unable  to  take  the  first 
in  the  manner  in  which  he  has  just  explained  it. 
But  there  seems  to  me  to  be  a  mean  position.  He 
proves  that  I  ought  to  choose  the  latter  because  I 
consider  the  individual  concept  of  Adam  as  possible 
when  I  maintain  that  among  an  infinity  of  possible 


108  CORRESPONDENCE. 

concepts  God  has  selected  a  certain  Adam,  while 
the  possible  concepts  in  themselves  do  not  at  all 
depend  upon  the  free  decrees  of  God. 

But  here  I  must  needs  explain  myself  a  little 
better.  I  say,  therefore,  that  the  connection 
between  Adam  and  human  events  is  not  indepen- 
dent of  all  the  free  decrees  of  God,  but  also,  that  it 
does  not  depend  upon  them  in  such  a  way  that  each 
event  could  happen  or  be  foreseen  only  because  of 
a  particular  primitive  decree  made  about  it.  I 
think  that  there  are  only  a  few  primitive  free 
decrees  regulating  the  sequence  of  things  which 
could  be  called  the  laws  of  the  universe  and  which, 
being  joined  to  the  free  decree  to  create  Adam, 
bring  about  the  consequences.  In  very  much  the 
same  way  as  but  few  hypotheses  are  called  for  to 
explain  phenomenon.  I  will  make  this  clearer  in 
what  follows. 

As  regards  the  objection  that  possibles  are  inde- 
pendent of  the  decrees  of  God  I  grant  it  of  actual 
decrees  (although  the  Cartesians  do  not  at  all  agree 
to  this),  but  I  maintain  that  the  possible  individual 
concepts  involve  certain  possible  free  decrees;  for 
example,  if  this  world  was  only  possible,  the  indi- 
vidual concept  of  a  particular  body  in  this  world 
would  involve  certain  movements  as  possible,  it 
would  also  involve  the  laws  of  motion,  which  are  the 
free  decrees  of  God;  but  these,  also,  only  as  possi- 
bilities. Because,  as  there  are  an  infinity  of  pos- 
sible worlds,  there  are  also  an  infinity  of  laws, 
certain  ones  appropriate  to  one;  others,  to  another, 
and  each  possible  individual  of  any  world  involves 
in  its  concept  the  laws  of  its  world. 

The   same   can   be   said    of   miracles,   or   of   the 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         109 

extraordinary  operations  of  God.  These  are  a  part 
of  the  general  order  and  conform  to  the  principal 
purposes  of  God  and  consequently,  are  involved  in 
the  concept  of  this  universe,  which  is  a  result  of 
these  designs.  Just  as  the  idea  of  a  building  results 
from  the  purposes  or  plans  of  him  who  undertakes 
it,  so  the  idea  or  concept  of  this  world  is  a  result  of 
the  designs  of  God  considered  as  possible.  For 
everything  should  be  explained  by  its  cause  and  of 
the  universe  the  cause  is  found  in  the  purposes  of 
God.  Now,  each  individual  substance,  in  my  opin- 
ion, expresses  the  whole  universe,  according  to  a 
certain  aspect  and  consequently  it  also  expresses 
the  so-called  miracles.  All  this  ought  to  be  under- 
stood in  regard  to  the  general  order,  in  regard  to  the 
plans  of  God,  in  regard  to  the  sequences  of  this  uni- 
verse, in  regard  to  the  individual  substance  and  in 
regard  to  miracles,  whether  they  are  taken  in  the 
actual  condition  or  whether  they  are  considered  sub 
ratione  possibilitatis.  For  another  possible  world 
would  have  all  such  orderings,  according  to  its  own 
manner,  although  the  plans  of  ours  were  preferred. 

It  can  be  seen  also  from  what  I  have  just  said  con- 
cerning the  plans  of  God  and  concerning  the  prim- 
itive laws,  that  this  universe  has  a  certain  primary 
or  primitive  concept,  from  which  the  particular 
events  are  only  the  consequences — with  the  excep- 
tion of  liberty  and  contingencies,  whose  certitude, 
however,  is  not  affected,  because  the  certitude  of 
events  is  based  in  part  upon  free  acts.  Now  every 
individual  substance  of  this  universe  expresses  in  its 
concept  the  universe  into  which  it  has  entered.  Not 
only  the  supposition  that  God  has  resolved  to  create 
this  Adam  but  also  any  other  individual  substance 


IIO  CORRESPONDENCE. 

that  may  be,  involves  the  resolves  for  all  the  rest, 
because  this  is  the  nature  of  an  individual  sub- 
stance, namely,  to  have  so  complete  a  concept  that 
from  it  may  be  deduced  all  that  can  be  attributed  to 
it,  and  even  the  whole  universe,  because  of  the 
inter-connection  between  things;  nevertheless,  to 
speak  more  strictly,  it  must  be  said  that  it  is  not  so 
much  because  God  has  resolved  to  create  this  Adam 
that  he  made  all  his  other  resolutions,  but  because 
the  resolution  which  he  made  in  regard  to  Adam, 
as  also  that  which  he  made  in  regard  to  other  par- 
ticular things,  are  consequences  of  the  resolve  which 
he  made  in  regard  to  the  whole  universe  and  to  the 
principal  designs  which  determine  its  primary  con- 
cept; these  resolves  have  established  this  general 
and  unchangeable  order  to  which  everything  con- 
forms without  even  excepting  the  miracles  which 
are  doubtless  conformable  to  the  principal  designs  of 
God,  although  the  particular  regulations  which  are 
called  the  laws  of  Nature  are  not  always  observed. 

I  have  said  that  the  supposition  from  which  all 
human  events  can  be  deduced  is  not  simply  that  of 
the  creation  of  an  undetermined  Adam  but  the  crea- 
tion of  a  particular  Adam,  determined  to  all  the  cir- 
cumstances, chosen  out  of  an  infinity  of  possible 
Adams.  This  has  given  M.  Arnaud  opportunity  to 
object,  not  without  reason,  that  it  is  as  little  pos- 
sible to  conceive  several  Adams,  understanding 
Adam  as  a  particular  nature,  as  to  conceive  of 
several  me's.  I  agree,  but  yet,  in  speaking  of 
several  Adams,  I  do  not  take  Adam  for  a  deter- 
mined individual.  I  must,  therefore,  explain. 
This  is  what  I  meant.  When  we  consider  in  Adam 
a  part  of  his  predicates,  for  example,  that  he  was  the 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS.          Ill 

first  man,  put  into  a  garden  of  enjoyment,  and  that, 
from  his  side,  God  took  a  woman,  and,  if  we  con- 
sider similar  things,  conceived  sub  ratione  generali- 
tatis  (that  is  to  say,  without  mentioning  Eve  or 
Paradise,  or  the  other  circumstances  which  consti- 
tute his  individuality),  and  if  we  call  the  person  to 
whom  these  predicates  are  attributed  Adam,  all  this 
does  not  suffice  to  determine  the  individual,  for 
there  might  be  an  infinity  of  Adams,  that  is  to  say, 
of  possible  persons  to  whom  these  would  apply  who 
would,  nevertheless,  differ  among  themselves.  Far 
from  disagreeing  with  M.  Arnaud,  in  what  he  says 
against  the  plurality  of  the  same  individual,  I 
would  myself,  employ  the  idea  to  make  it  clearer 
that  the  nature  of  an  individual  should  be  complete 
and  determined.  I  am  quite  convinced  in  regard  to 
what  St.  Thomas  has  taught  about  intelligences, 
and  what  I  hold  to  be  a  general  truth,  namely, 
that  it  is  not  possible  for  two  individuals  to  exist 
wholly  alike,  that  is,  differing  solo  numero.  We 
must,  therefore,  not  conceive  of  a  vague  Adam  or 
of  a  person  to  whom  certain  attributes  of  Adam 
appertain  when  we  try  to  determine  him,  if  we 
would  hold  that  all  human  events  follow  from  the 
one  presupposition,  but  we  must  attribute  to  him  a 
concept  so  complete  that  all  which  can  be  attributed 
to  him  may  be  derived  from  his.  Now,  there  is  no 
ground  for  doubting  that  God  can  form  such  a  con- 
cept or,  rather,  that  he  finds  it  already  formed  in 
the  region  of  possibilities,  that  is  to  say,  in  his 
understanding. 

It  follows,  also,  that  if  he  had  had  other  circum- 
stances, this  would  not  have  been  our  Adam,  but 
another,  because  nothing  prevents  us  from  saying 


112  CORRESPONDENC  E. 

that  this  would  be  another.  He  is,  therefore, 
another.  It  indeed  appears  to  us  that  this  block  of 
marble  brought  from  Genoa  would  be  wholly  the 
same  if  it  had  been  left  there,  because  our  senses 
cause  us  to  judge  only  superficially,  but  in  reality, 
because  of  the  inter-connection  of  things,  the  uni- 
verse, with  all  its  parts,  would  be  wholly  different 
and  would  have  been  wholly  different  from  the  very 
commencement  if  the  least  thing  in  it  happened 
otherwise  than  it  has.  It  is  not  because  of  their 
inter-connection  that  events  are  necessary,  but  it  is 
because  they  are  certain  after  the  choice  which  God 
made  of  this  possible  universe  whose  concept  con- 
tains this  sequence  of  things.  I  hope  that  what  I 
am  about  say  will  enable  M.  Arnaud  himself  to 
agree  to  this. 

Let  a  certain  straight  line,  ABC,  represent  a 
certain  time,  and  let  there  be  a  certain  individual 
substance,  for  example,  myself,  which  lasts  or 
exists  during  this  period.  Let  us  take  then,  first, 
the  me  which  exists  during  the  time  A  B,  and 
again  the  me  which  exists  during  the  time  B  C. 
Now,  since  people  suppose  that  it  is  the  same  indi- 
vidual substance  which  perdures,  or  that  it  is  the 
me  which  exists  in  the  time  A  B  while  at  Paris 
and  which  continues  to  exist  in  the  time  B  C 
while  in  Germany,  it  must  needs  be  that  there 
should  be  some  reason  why  we  can  veritably  say 
that  I  perdure,  or,  to  say,  that  the  me  which 
was  at  Paris  is  now  in  Germany,  for,  if  there 
were  no  reason,  it  would  be  quite  right  to  say  that 
it  was  another.  To  be  sure,  my  inner  experience 
convinces  me  a  posteriori  of  this  identity  but  there 
must  be  also  some  reason  a  priori.  It  is  not  pos- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          113 

sible  to  find  any  other  reason,  excepting  that  my 
attributes  of  the  preceding  time  and  state,  as  well 
as  the  attributes  of  the  succeeding  time  and  state 
are  predicates  of  the  same  subject;  insunt  eidem 
subjecto.  Now,  what  is  it  to  say  that  the  predicate 
is  in  the  subject  if  not  that  the  concept  of  the 
predicate  is  found  in  some  sort  involved  in  the  con- 
cept of  the  subject?  Since  from  the  very  time  that 
I  began  to  exist  it  could  be  said  of  me  truly  that 
this  or  that  would  happen  to  me,  we  must  grant  that 
these  predicates  were  principles  involved  in  the  sub- 
ject or  in  my  complete  concept,  which  constitutes 
the  so-called  me,  and  which  is  the  basis  of  the  inter- 
connection of  all  my  different  states.  These,  God 
has  known  perfectly  from  all  eternity.  After  this  I 
think  that  all  doubts  ought  to  disappear,  for  when  I 
say  that  the  individual  concept  of  Adam  involves 
all  that  will  ever  happen  to  him  I  mean  nothing  else 
than  what  the  philosophers  understand  when  they 
say  that  the  predicate  is  contained  in  the  subject  of 
true  propositions.  It  is  true  that  the  consequences 
of  so  clear  a  teaching  are  paradoxical,  but  it  is  the 
fault  of  the  philosophers  who  have  not  sufficiently 
followed  out  perfectly  clear  notions. 

Now  I  think  that  M.  Arnaud,  discerning  and  fair 
as  he  is,  will  not  find  my  proposition  so  strange  and, 
although  he  may  not  be  able  to  approve  of  it 
entirely,  yet  I  almost  flatter  myself  with  having  his 
approbation.  I  agree  with  what  he  judiciously  has 
added,  in  regard  to  the  care  that  must  be  employed 
in  having  recourse  to  knowledge  of  divine  things  for 
the  determination  of  what  we  should  decide  con- 
cerning the  concepts  of  mundane  things.  But  rf 
properly  understood,  what  I  have  just  said  must  be 


114  CORRESPONDENCE. 

said  even  when  we  speak  of  God  only  as  much  as  is 
necessary.  For,  even  if  we  should  not  say  that 
God,  in  considering  Adam,  whom  he  resolved  to 
create,  saw  all  the  events  which  will  happen  to  him, 
it  is  enough  that  we  can  always  prove  that  he  had  a 
complete  concept  of  this  Adam  which  involved 
these  events.  Because  all  the  predicates  of  Adam, 
either  depend  upon  the  other  predicates  of  the  same 
Adam,  or  they  do  not.  Putting  one  side  those 
which  depend  upon  others,  we  have  only  to  gather 
together  all  the  primitive  predicates  in  order  to  form 
a  concept  of  Adam  sufficiently  complete  to  deduce 
whatever  will  happen  to  him  in  so  far  as  a  reason  is 
needed.  It  is  evident  that  God  can  discover,  and 
indeed  effectively  conceive  such  a  concept  sufficient 
to  assign  a  reason  to  all  the  phenomena  pertaining 
to  Adam;  but  not  less  clear  is  it,  however,  that  this 
concept  is  possible  in  itself.  Truly,  we  must  not 
submerge  ourselves  more  than  necessary,  when  we 
investigate,  in  divine  knowledge  and  will,  because 
of  the  great  difficulties  which  there  are  there. 
Nevertheless,  we  may  explain  what  we  have  derived 
for  our  question  from  such  a  source  without  enter- 
ing into  those  difficulties  which  M.  Arnaud  men- 
tions; for  instance,  the  difficulty  of  understanding 
how  the  simplicity  of  God  is  reconcilable  with  cer- 
tain things  which  we  are  obliged  to  distinguish  from 
it.  It  is  also  very  difficult  to  explain  perfectly  how 
God  has  knowledge  which  he  was  able  not  to  have, 
that  is,  the  knowledge  of  prevision,  for,  if  future 
contingencies  did  not  exist,  God  would  have  no 
vision  of  them.  It  is  true  that  he  might  have  sim- 
ple knowledge  of  future  contingencies  which  would 
become  prevision  when  joined  to  his  will  so  that  the 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          11$ 

difficulty  above  would  be  reduced  to  the  difficulties 
present  in  conceiving  of  the  will  of  God.  That  is 
to  say,  the  question  how  God  is  free  to  will.  This, 
without  doubt,  passes  our  ken,  but  it  is  not  essen- 
tial to  understand  it  in  order  to  solve  our  question. 
In  regard  to  the  manner  in  which  we  conceive 
that  God  acts  when  he  chooses  the  best  among 
several  possibilities,  M.  Arnaud  has  reason  to  find 
some  obscurity.  He  seems,  nevertheless,  to  recog- 
nize that  I  am  inclined  to  think  that  there  are  an 
infinity  of  possible  first  men,  each  one  with  a  great 
sequence  of  personages  and  events,  and  that  God 
chose  among  them  the  one  which  pleased  him, 
together  with  his  sequence.  This  is  not,  therefore, 
so  strange  as  it  appears  at  first.  It  is  true,  M. 
Arnaud  says  he  is  inclined  to  think  that  substances 
which  are  purely  possible  are  only  chimeras.  In 
regard  to  this,  I  do  not  wish  to  dispute,  but  I  hope 
that,  nevertheless,  he  will  grant  m'e  as  much  as  I 
have  need  of.  I  agree  that  there  is  no  other  reality 
in  pure  possibilities  than  what  they  have  in  the 
divine  understanding,  and  we  see,  therefore,  that  M. 
Arnaud  will  be  obliged  himself  to  have  recourse 
to  the  divine  knowledge  in  order  to  explain  them, 
while  he  seems  above  to  have  wished  that  they 
might  be  sought  in  "themselves.  When  I  grant 
further  what  M.  Arnaud  is'  convinced  of  and  what  I 
do  not  deny,  that  we  conceive  nothing  as  possible 
excepting  through  the  ideas  which  are  actually 
found  in  the  things  which  God  has  created,  this 
does  not  at  all  injure  my  position,  for,  in  speaking 
of  possibilities,  I  am  content  if  true  propositions 
may  be  formed  concerning  them.  For  example,  if 
there  were  no  perfect  square  in  the  world,  we  should, 


Il6  CORRESPONDENCE. 

nevertheless,  see  that  no  contradiction  was  implied 
in  the  idea.  If  we  wish  to  reject  absolutely  the 
pure  possibles,  contingencies  will  be  destroyed, 
because  if  nothing  is  possible  except  what  God  has 
actually  created  then  what  God  has  actually  created 
would  be  necessary  in  case  he  resolved  to  create 
anything. 

Finally,  I  agree  that  in  order  to  determine  the 
concept  of  an  individual  substance  it  is  good  to  con- 
sult the  concept  which  I  have  of  myself,  just  as  the 
specific  concept  of  the  sphere  must  be  consulted  in 
order  to  determine  its  properties.  Nevertheless, 
there  is  a  great  difference  in  the  two  cases  for  the 
concept  of  myself  and  of  any  other  individual  sub- 
stance, is  infinitely  more  extended  and  more  diffi- 
cult to  understand  than  is  a  specific  concept  like 
that  of  a  sphere  which  is  only  incomplete.  It  is 
not  sufficient  that  I  feel  myself  as  a  substance  which 
thinks;  1  must  also  distinctly  conceive  whatever  dis- 
tinguishes me  from  all  other  spirits.  But  of  this  I 
have  only  a  confused  experience. 

Therefore,  although  it  is  easy  to  determine  that 
the  number  of  feet  in  the  diameter  is  not  involved 
in  the  concept  of  the  sphere  in  general,  it  is  not  so 
easy  to  decide  if  the  journey  which  I  intend  to  make 
is  involved  in  my  concept;  otherwise,  it  would  be  as 
easy  for  us  to  become  prophets  as  to  be  Geometers. 
I  am  uncertain  whether  I  will  make  the  journey  but 
I  am  not  uncertain  that,  whether  I  make  it  or  no,  I 
will  always  be  myself.  Such  human  previsions  are 
not  the  same  as  distinct  notions  or  distinct  knowl- 
edge. They  appear  to  us  undetermined  because  the 
evidences  or  marks  which  are  found  in  our  sub- 
stance are  not  recognizable  by  us.  Very  much  as 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         117 

those  who  regard  sensations  merely,  ridicule  one 
who  says  that  the  slightest  movement  is  communi- 
cated as  far  as  matter  extends,  because  experience 
alone  could  not  demonstrate  this  to  them.  When, 
however,  they  consider  the  nature  of  motion  and 
matter  they  are  convinced  of  it.  It  is  the  same  here 
when  the  confused  experience,  which  one  has  of  his 
individual  concept  in  particular,  is  consulted.  He 
does  not  take  care  to  notice  this  inter-connection  of 
events,  but,  when  he  considers  general  and  distinct 
notions  which  enter  into  them,  he  finds  the  connec- 
tion. In  fact,  when  I  consult  the  conception  which 
I  have  of  all  true  propositions,  I  find  that  every 
necessary  or  contingent  predicate,  every  past,  pres- 
ent, or  future,  predicate,  is  involved  in  the  concept 
of  the  subject,  and  I  ask  no  more. 

I  think,  indeed,  that  this  will  open  to  us  a  means 
of  reconciliation.  For,  I  think,  that  M.  Arnaud 
disliked  to  grant  this  proposition,  only  because  he 
understood  the  connection  which  I  held  to,  both  as 
intrinsic  and  necessary  at  the  same  time,  while  I 
hold  it  indeed  as  intrinsic  but  not  at  all  as  neces- 
sary. I  have  now  sufficiently  explained  that  it  is 
founded  upon  free  decrees  and  free  acts.  I  mean 
no  other  connection  between  the  subject  and  the 
predicate  than  that  which  there  is  in  the  most  con- 
tingent of  true  propositions.  That  is  to  say,  I  mean 
that  there  is  always  something  to  be  conceived  of  in 
the  subject  which  serves  to  give  the  reason  why  this 
predicate  or  event  pertains  to  it  or  why  a  certain 
thing  has  happened  to  it  rather  than  not. 

These  reasons  of  contingent  truths,  however, 
bring  about  results  without  necessitation.  It  is 
therefore  true  that  I  am  able  not  to  make  this 


Il8  CORRESPONDENCE. 

journey,  but  it  is  certain  that  I  will  make  it.  This 
predicate  or  event  is  not  connected  certainly  with 
my  other  predicates  conceived  of  incompletely  or 
sub  ratione  generalitatis ;  but  it  is  certainly  con- 
nected with  a  complete  individual  concept  because 
I  presuppose  that  this  concept  is  constructed 
expressly  in  such  a  way  that  from  it  may  be  deduced 
all  that  happens  to  me.  This  concept  is  found  doubt- 
less a  parte  rei  and  is  properly  a  concept  of  myself 
which  I  find  under  different  conditions,  since  it  is 
this  concept  alone  that  can  include  them  all. 

I  have  so  much  deference  for  M.  Arnaud  and  such 
a  good  opinion  of  his  judgment,  that  I  easily  give 
up  my  opinions  or  at  least  my  expressions  as  soon 
as  I  see  that  he  finds  something  objectionable  in 
them.  It  is  for  this  reason  that  I  have  carefully  fol- 
lowed the  difficulties  which  he  put  forward  and  now, 
after  I  have  attempted  to  meet  them  in  good  faith, 
it  seems  to  me  that  I  am  still  not  far  from  those 
very  positions. 

The  proposition  which  we  are  discussing  is  of 
great  importance  and  should  be  firmly  established, 
since  from  it  follows  that  every  soul  is  a  world  by 
itself, independent  of  everything  excepting  God;  that 
it  is  not  only  immortal,  and,  so  to  speak,  permanent, 
but  that  it  bears  in  its  substance  traces  of  everything 
that  happens  to  it.  From  it  can  be  deduced  also  in 
what  the  inter-activities  of  substances  consist  and 
particularly  the  union  of  soul  and  body.  This 
inter-activity  is  not  brought  about  according  to  the 
usual  hypothesis  of  the  physical  influence  of  one 
substance  upon  another  because  every  present  state 
of  a  substance  comes  to  it  spontaneously  and  is  only 
a  sequence  of  its  preceding  state.  No  more  is  the 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         1 19 

inter-activity  accounted  for  by  the  hypothesis  of 
occasional  causes  as  though  God  intervened  differ- 
ently for  ordinary  events  than  when  he  preserved 
every  substance  in  its  course;  and  as  though  God 
whenever  something  happened  in  the  body  aroused 
thoughts  in  the  soul  which  would  thus  change  the 
course  that  the  soul  would  itself  have  taken  with- 
out this  intervention.  The  inter-activity  is  in 
accordance  with  the  hypothesis  of  concomitants 
which,  to  me,  appears  demonstrative.  That  is  to 
say,  each  substance  expresses  the  whole  sequence  of 
the  universe  according  'to  the  view  or  relation  that 
is  appropriate  to  it.  Whence  it  follows  that  sub- 
stances agree  perfectly  and  when  we  say  that  one 
acts  upon  another,  we  mean  that  the  distinct  expres- 
sion of  the  one  which  is  acted  upon  diminishes,  but 
of  the  one  which  acts,  augments,  conformably  to 
the  sequence  of  thoughts  which  its  concept  involves. 
For,  although  each  substance  expresses  everything, 
we  are  justified  in  attributing  to  it  ordinarily  only 
the  expressions  which  are  most  evident  in  its  partic- 
ular relation. 

Finally,  I  think  after  this,  that  the  propositions 
contained  in  the  abstract  sent  to  M.  Arnaud  will 
appear  not  only  more  intelligible  but,  perhaps,  bet- 
ter founded  and  more  important  than  might  have 
been  thought  at  first. 

IX 
Leibniz  to  Arnauld. 

Hanover,  July  14,  1686. 
Monsieur: 

As  I  have  great  deference  for  your  judgment,  I 
was  glad  to  see  that  you  moderated  your  censure 


120  CORRESPONDENCE. 

after  having  seen  my  explanation  of  that  proposi- 
tion which  I  thought  important  and  which  appeared 
strange  to  you:  "That  the  individual  concept  of 
each  person  involves  once  for  all,  all  that  will  ever 
happen  to  him."  From  this  at  first  you  drew  this 
consequence,  namely,  that  from  the  single  supposi- 
tion that  God  resolved  to  create  Adam,  all  the  rest 
of  the  human  events  which  happened  to  Adam  and 
to  his  posterity  would  have  followed  by  a  fatalistic 
necessity,  without  God's  having  the  freedom  to 
make  a  change  any  more  than  he  would  have  been 
able  not  to  create  a  creature  capable  of  thought 
after  having  resolved  to  create  me. 

To  which  I  replied,  that  the  designs  of  God  re- 
garding all  this  universe  being  inter-related  conform- 
ably to  his  sovereign  wisdom,  he  made  no  resolve 
in  respect  to  Adam  without  taking  into  considera- 
tion everything  which  had  any  connection  with  him. 
It  was  therefore  not  because  of  the  resolve  made  in 
respect  to  Adam  but  because  of  the  resolution  made 
at  the  same  time  in  regard  to  all  the  rest  (to  which 
the  former  involves  a  perfect  relationship),  that 
God  formed  the  determination  in  regard  to  all 
human  events.  In  this  it  seems  to  me  that  there  was 
no  fatalistic  necessity  and  nothing  contrary  to  the 
liberty  of  God  any  more  than  there  is  in  this  gener- 
ally accepted  hypothetical  necessity  which  God  is 
under  of  carrying  out  what  he  has  resolved  upon. 

You  accept,  M.,  in  your  reply,  this  inter-relation 
of  the  divine  resolves  which  I  put  forward  and  you 
even  have  the  sincerity  to  acknowledge  that  at  first 
you  understood  my  proposition  wholly  in  a  differ- 
ent sense,  "Because  it  is  not  customary  for  exam- 
ple" (these  are  your  words),  "to  consider  the  specific 


LIIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          121 

concept  of  a  sphere  in  relation  to  its  representation 
in  the  Divine  understanding  but  in  relation  to  that 
which  it  is  itself."  And  you  thought  "that  it  was 
thus  also  with  respect  to  the  individual  concept  of 
each  person." 

On  my  part,  I  thought  that  complete  and  com- 
prehensible concepts  are  represented  in  the  divine 
understanding  as  they  are  in  themselves  but  now 
that  you  know  what  my  thought  is,  you  say  it  is 
sufficient  to  conform  to  it  and  to  inquire  if  it 
removes  the  difficulty.  It  seems  then  that  you 
realize  that  my  position  as  explained  in  this  way, 
to  mean  complete  and  comprehensive  concepts 
such  as  they  are  in  the  divine  understanding,  is  not 
only  innocent  but  is,  indeed,  right,  for  here  are  your 
words,  "I  agree  that  the  knowledge  which  God  had 
of  Adam  when  he  resolved  to  create  him  involved 
everything  that  has  happened  to  him  and  all  that 
has  happened  and  will  happen  to  his  posterity,  and 
therefore,  taking  the  individual  concept  of  Adam  in 
this  sense,  what  you  say  is  very  certain."  We  will 
go  on  to  see  very  soon  in  what  the  difficulty  which 
you  still  find  consists.  Yet  I  will  say  one  word  in 
regard  to  the  cause  for  the  difference  which  there 
is  here  between  concepts  of  space  and  those  of  indi- 
vidual substances,  rather  in  relation  to  the  divine 
will  than  in  relation  to  the  simple  understand- 
ing. This  difference  is  because  the  most  abstract 
specific  concepts  embrace  only  necessary  or  eter- 
nal truths  which  do  not  depend  upon  the  decrees 
of  God  (whatever  the  Cartesians  may  say  about  this 
'whom  it  seems  you  have  not  followed  at  this  point), 
but  the  concepts  of  individual  substances  which  are 
complete,  and  sufficient  to  identify  entirely  their 


122  CORRESPONDENCE. 

subjects  and  which  involve  consequently  truths  that 
are  contingent  or  of  fact,  namely,  individual  circum- 
stances of  time,  of  space,  etc. — such  substances,  I  say, 
should  also  involve  in  their  concept  taken  as  pos- 
sible, the  free  decrees  or  will  of  God,  likewise  taken 
as  possible,  because  these  free  decrees  are  the  prin- 
cipal sources  for  existences  or  facts  while  essences 
are  in  the  divine  understanding  before  his  will  is 
taken  into  consideration. 

This  will  suffice  to  make  clearer  all  the  rest  and  to 
meet  the  difficulties  which  still  seem  to  remain  in 
my  explanation.  For  you  continue  in  this  way: 
"But  it  seems  that  after  that  the  question  still 
remains,  and  here  is  my  difficulty,  whether  the  con- 
nection between  these  objects,  I  mean  Adam  and 
human  events,  is  such,  of  itself,  independently  of 
all  the  free  decrees  of  God  or  if  it  is  dependent  upon 
them.  That  is  to  say,  whether  God  knows  what 
will  happen  to  Adam  and  his  posterity  only  because 
of  the  free  decrees  by  which  God  has  ordained  all 
that  will  happen  to  them,  or  if  there  is,  independ- 
ently of  these  decrees,  between  Adam  on  the  one 
hand  and  that  which  has  happened  to  him  and  will 
happen  to  him  and  to  his  posterity  on  the  other,  an 
intrinsic  and  necessary  connection."  It  seems  to 
you  that  I  will  take  the  latter  alternative  because  I 
have  said,  "That  God  has  found  among  the  possi- 
bilities an  Adam  accompanied  by  certain  individual 
circumstances  and  who,  among  other  predicates,  has 
also  this  one  of  having  in  time  a  certain  pos- 
terity." Now  you  suppose  that  I  agree  that  the 
possibilities  are  possible  before  all  the  free  decrees 
of  God;  supposing,  therefore,  this  explanation  of 
my  position  according  to  the  latter  alternative,  you 


LEIBNIZ.       ARNAULD.       HISSEN-RHEINFELS.  123 

think  that  it  has  insurmountable  difficulties.  For 
there  are,  as  you  say  with  good  reason,  "an  infinity 
of  human  events  that  happen  by  the  expressly  par- 
ticular ordinances  of  God.  Among  others,  the  Jew- 
ish and  Christian  religions  and,  above  all,  the  Incar- 
nation of  the  divine  word.  And  I  do  not  know  how 
one  could  say  that  all  this  (which  has  happened  by 
the  free  decrees  of  God),  could  be  involved  in  the 
individual  concept  of  the  possible  Adam.  What- 
ever is  considered  as  possible  ought  to  have  every- 
thing that  could  be  conceived  as  being  under  this 
concept,  independently  of  the  divine  decrees." 

I  wish  to  state  your  difficulty  exactly,  Monsieur, 
and  this  is  the  way  in  which  I  hope  to  satisfy  it 
entirely  to  your  own  taste.  For  it  must  needs  be 
that  it  can  be  resolved,  since  we  cannot  deny  that 
there  is  truly  a  certain  concept  of  Adam  accom- 
panied by  all  its  predicates  and  conceived  as  pos- 
sible, which  God  knew  before  resolving  to  create 
him,  as  you  have  just  admitted.  I  think,  therefore, 
that  the  dilemma  of  the  alternative  explanation 
which  you  have  proposed  may  have  a  mean,  and 
the  connection  which  I  conceive  of  between  Adam 
and  human  events  is  intrinsic  but  it  is  not  neces- 
sarily independent  of  the  free  decrees  of  God 
because  the  free  decrees  of  God  taken  as  possible 
enter  into  the  concept  of  the  possible  Adam,  and 
when  these  same  decrees  become  actual  they  are 
the  cause  of  the  actual  Adam.  I  agree  with  you, 
in  opposition  to  the  Cartesians,  that  the  possibles 
are  possible  before  all  the  actual  decrees  of  God,  but 
the  decrees  themselves,  must  be  regarded  also  as 
possibles.  For  the  possibilities  of  the  individual  or 
of  contingent  truths  involve  in  their  concept  the 


1 24  CORRESPONDENCE. 

possibility  of  their  causes,  that  is  to  say,  the  free 
decrees  of  God  in  which  they  are  different  from 
generic  possibilities  or  from  eternal  truths.  These 
latter  depend  solely  upon  the  understanding  of  God 
without  presupposing  any  will,  as  I  have  explained 
it  above. 

This  might  be  enough,  but  in  order  to  make 
myself  better  understood,  I  will  add  that  1  think 
there  were  an  infinity  of  possible  ways  of  creating 
the  world  according  to  the  different  plans  which 
God  might  have  formed  and  that  each  possible 
world  depends  upon  certain  principal  plans  or 
designs  of  God  that  are  his  own;  that  is  to  say, 
upon  certain  primary  free  decrees  conceived  sub 
ratione  possibilitatis^  or  upon  certain  laws  of  the 
general  order  of  this  possible  universe  with  which 
they  agree  and  whose  concept  they  determine.  At 
the  same  time  they  determine  the  concepts  of  all 
individual  substances  which  ought  to  enter  into  this 
same  universe.  Everything,  therefore,  is  in  order 
even  including  miracles,  although  these  latter  are 
contrary  to  certain  subordinate  regulations  or  laws 
of  nature.  Thus,  all  human  events  cannot  fail  to 
happen  as  they  have  actually  happened,  supposing 
that  the  choice  of  Adam  was  made.  But  this  is  so, 
not  so  much  because  of  the  concept  of  the  indi- 
vidual Adam,  although  this  concept  involves  them, 
but  because  of  the  purposes  of  God,  which  also 
enter  into  this  individual  concept  of  Adam  and 
determine  the  concept  of  the  whole  universe.  These 
purposes  determine,  consequently,  as  well  the  con- 
cept of  Adam  as  the  concepts  of  all  the  other  indi- 
vidual substances  of  this  universe,  because  each 
individual  substance  expresses  the  whole  universe, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          125 

of  which  it  is  a  part  according  to  a  certain  relation, 
through  the  connection  which  there  is  between  all 
things,  and  this  connection  is  owing  to  the  connec- 
tion of  the  resolutions  or  plans  of  God. 

I  find  that  you  bring  forward  another  objection, 
Monsieur,  which  does  not  depend  upon  the  conse- 
quences, apparently  contradicting  freedom,  as  was 
the  objection  which  I  just  met,  but  which  depends 
upon  the  matter  itself  and  upon  the  idea  which  we 
have  of  an  individual  substance.  Because,  since  I 
have  the  idea  of  an  individual  substance,  that  is  to 
say  of  myself,  it  seems  to  you  that  we  must  seek 
what  is  meant  by  an  individual  concept  in  this  idea 
and  not  in  the  way  in  which  God  conceives  of  indi- 
viduals; and  just  as  I  have  only  to  consult  the 
specific  concept  of  the  sphere  in  order  to  decide  if 
the  number  of  feet  in  the  diameter  is  not  determined 
by  this  concept,  in  the  same  way  you  say  I  find 
clearly  in  the  individual  concept  which  I  have  of 
myself  that  I  will  be  myself,  in  either  case  whether 
I  make  or  do  not  make  the  journey  which  I  intend. 

In  order  to  make  my  reply  clear,  I  agree  that  the 
connection  of  events,  although  it  is  certain,  is  not 
necessary,  and  that  I  am  at  liberty  either  to  make 
or  not  to  make  the  journey,  for,  although  it  is 
involved  in  my  concept  that  I  will  make  it,  it  is  also 
involved  that  I  will  make  it  freely.  And  there  is 
nothing  in  me  of  all  that  can  be  conceived  sub 
ratione  generalitatis,  whether  of  essence  or  of 
specific  or  incomplete  concepts  from  which  it  can  be 
deduced  that  1  will  make  it  necessarily.  While,  on 
the  other  hand,  from  the  fact  that  I  am  a  man,  the 
conclusion  can  be  drawn  that  I  am  capable  of  think- 
ing, and  consequently,  if  I  do  not  make  this  journey, 


126  CORRESPONDENCE. 

this  will  be  against  no  eternal  or  necessary  truth. 
Still,  since  it  is  certain  that  I  will  make  it  there 
must  be  indeed  some  connection  between  the  me 
which  is  the  subject,  and  the  carrying  out  of  the 
journey,  which  is  the  predicate.  The  concept  of 
the  predicate  is  always  in  the  subject  of  a  true  propo- 
sition. There  is,  therefore,  an  omission,  if  I  do 
make  it,  which  will  destroy  my  individual  or  com- 
plete concept,  or  which  would  destroy  what  God 
conceives  or  conceived  in  regard  to  me  even  before 
resolving  to  create  me.  For  this  concept  involves, 
sub  ratione  possibilitatis,  the  existences  or  the  truths 
of  fact  or  the  decrees  of  God  upon  which  the  facts 
depend. 

I  agree,  also,  that  in  order  to  determine  the  con- 
cept of  an  individual  substance  it  is  good  to  consult 
that  which  I  have  of  myself,  as  we  must  consult  a 
specific  concept  of  a  sphere  in  order  to  determine 
its  properties.  Nevertheless,  there  is  between  the 
two  cases  a  great  difference,  for  the  concept  of 
myself  in  particular  and  of  any  other  individual 
substance  is  infinitely  more  extensive  and  more 
difficult  to  understand  than  is  a  specific  concept, 
such  as  a  sphere,  which  is  only  incomplete  and  does 
not  involve  all  the  practically  necessary  circum- 
stances to  get  at  a  particular  sphere.  It  is  not 
enough  in  order  to  understand  what  the  me  is  that  I 
am  sensible  of  a  subject  which  thinks,  I  must  also 
conceive  distinctly  of  all  that  which  distinguishes 
me  from  other  possible  spirits  and  of  this  latter  I 
have  only  a  confused  experience.  Therefore,  it  is 
easy  to  determine  that  the  number  of  feet  in  the 
diameter  is  not  involved  in  the  notion  of  the  sphere 
in  general,  it  is  not  so  easy  to  determine  certainly, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          127 

although  we  can  decide  quite  probably  whether  the 
voyage  which  I  intend  to  make  is  involved  in  my 
concept;  were  it  not  so  it  would  be  as  easy  to  be  a 
prophet  as  to  be  a  geometer.  Nevertheless  as 
experience  is  unable  to  make  me  recognize  a  great 
number  of  insensible  things  in  the  body  in  regard 
to  which  the  general  consideration  of  the  nature  of 
bodies  and  of  movements  might  convince  me;  in 
the  same  way,  although  experience  cannot  make  me 
feel  all  that  is  involved  in  my  concept,  I  am  able  to 
recognize  in  general  that  everything  which  pertains 
to  me  is  involved  in  it  through  the  general  con- 
sideration of  an  individual  concept. 

Surely  since  God  can  form  and  does  actually  form 
this  complete  concept  which  involves  whatever  is 
sufficient  to  give  a  reason  for  all  the  phenomena 
that  happen  to  me,  the  concept  is  therefore  pos- 
sible. And  this  is  the  true  complete  concept  of 
that  which  I  call  the  me.  It  is  in  virtue  of  this  con- 
cept that  all  my  predicates  pertain  to  me  as  to  their 
subject.  We  are,  therefore,  able  to  prove  it  with- 
out mentioning  God,  except  in  so  far  as  it  is  neces- 
sary to  indicate  my  dependence.  This  truth  is 
expressed  more  forcefully  in  deriving  the  concept 
which  is  being  examined  from  the  divine  cognizance 
as  its  source.  I  grant  that  there  are  many  things  in 
the  divine  knowledge  which  we  are  unable  to  com- 
preherid  but  it  does  not  seem  to  me  that  we  must 
needs  go  into  them  to  solve  our  question.  Besides, 
if,  in  the  life  of  any  person,  and  even  in  the  whole 
universe  anything  went  differently  from  what  it 
has,  nothing  could  prevent  us  from  saying  that  it 
was  another  person  or  another  possible  universe 
which  God  had  chosen.  It  would  then  be  indeed 


128  CORRESPONDENCE. 

another  Individual.  There  must  then  be  some 
reason  a  priori  independent  of  my  existence  why  we 
may  truly  say  that  it  was  I  who  was  at  Paris  and 
that  it  is  still  I  and  not  another  who  am  now  in 
Germany  and  consequently  it  must  be  that  the  con- 
cept of  myself  unites  or  includes  different  condi- 
tions. Otherwise  it  could  be  said  that  it  is  not  the 
same  individual  although  it  appears  to  be  the  same 
and  in  fact  certain  philosophers  who  have  not 
understood  sufficiently  the  nature  of  substance 
and  of  individual  beings  or  of  beings  per  se 
have  thought  that  nothing  remained  actually  the 
same.  It  is  for  this,  among  other  reasons,  that  I 
have  come  to  the  conclusion  that  bodies  would 
not  be  substances  if  they  had  only  extension  in 
them. 

I  think,  Monsieur,  that  I  have  sufficiently  met 
the  difficulties  regarding  the  principal  proposition, 
but,  as  you  have  made  in  addition  some  important 
remarks  in  regard  to  certain  incidental  expressions, 
which  I  used,  I  will  attempt  to  explain  them  also. 
I  said  that  the  presupposition  from  which  all  human 
events  could  be  deduced,  was  not  that  of  the  crea- 
tion of  an  undetermined  Adam  but  of  the  creation 
of  a  certain  Adam  determined  in  all  circumstances, 
selected  out  of  an  infinity  of  possible  Adams.  In 
regard  to  this  you  make  two  important  remarks,  the 
one  against  the  plurality  of  Adams  and  the  other 
against  the  reality  of  substances  which  are  merely 
possible.  In  regard  to  the  first  point,  you  say  with 
good  reason  that  it  is  as  little  possible  to  think  of 
several  possible  Adams,  taking  Adam  for  a  partic- 
ular nature,  as  to  conceive  of  several  me's.  I  agree, 
but  in  speaking  of  several  Adams  I  do  not  take 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          129 

Adam  for  a  determined  individual  but  for  a  certain 
person  conceived  sub  ratione  generalitatis  under  the 
circumstances  which  appear  to  us  to  determine 
Adam  as  an  individual  but  which  do  not  actually 
determine  him  sufficiently.  As  if  we  should  mean 
by  Adam  the  first  man,  whom  God  set  in  a  garden 
of  pleasure  whence  he  went  out  because  of  sin,  and 
from  whose  side  God  fashioned  a  woman.  All  this 
would  not  sufficiently  determine  him  and  there 
might  have  been  several  Adams  separately  possible 
or  several  individuals  to  whom  all  that  would  apply. 
This  is  true,  whatever  finite  number  of  predicates 
incapable  of  determining  all  the  rest  might  be  taken, 
but  that  which  determines  a  certain  Adam  ought  to 
involve  absolutely  all  his  predicates.  And  it  is  this 
complete  concept  which  determines  the  particular 
individual.  Besides,  I  am  so  far  removed  from  a 
pluralistic  conception  of  the  same  individual  that  I 
agree  heartily  with  what  St.  Thomas  has  already 
taught  with  regard  to  intelligences  and  which  I 
hold  to  be  very  general,  namely,  that  it  is  not  pos- 
sible for  two  individuals  to  exist  entirely  alike  or 
differing  solo  numero. 

As  regards  the  reality  of  substances  merely  pos- 
sible, that  is  to  say,  which  God  will  never  create, 
you  say,  Monsieur,  that  you  are  very  much  inclined 
to  believe  that  they  are  chimeras.  To  which  I 
make  no  objection,  if  you  mean,  as  I  think,  that  they 
have  no  other  reality  than  what  comes  to  them  in 
the  divine  understanding  and  in  the  active  power  of 
God.  Nevertheless,  you  see  by  this,  Monsieur,  that 
we  are  obliged  to  have  recourse  to  the  divine  knowl- 
edge and  divine  power  in  order  to  explain  them 
well.  I  find  very  well  founded  that  which  you  say 


130  CORRESPONDENCE. 

afterwards,  "That  we  never  conceive  of  any  sub- 
stance merely  as  possible  except  under  the  idea  of 
a  particular  one  (or  through  the  ideas  understood  in 
a  particular  one)  of  those  which  God  has  created." 
You  say  also,  "We  imagine  that,  before  creating 
the  world,  God  looked  over  an  infinity  of  possible 
things  out  of  which  he  chose  certain  ones  and 
rejected  the  others,  certain  possible  Adams  (first 
men),  each  with  a  great  sequence  of  personages  with 
whom  he  has  an  intrinsic  connection;  and  we  sup- 
pose that  the  connection  of  all  these  other  things 
with  one  of  these  possible  Adams  (first  men)  is 
wholly  similar  to  that  which  the  actually  created 
Adam  had  with  all  his  posterity.  This  makes  us 
think  that  it  is  this  one  of  all  the  possible  Adams 
which  God  has  chosen  and  that  he  did  not  wish  any 
of  the  others."  In  this  you  seem  to  recognize  that 
those  ideas,  which  I  acknowledge  to  be  mine  (pro- 
vided that  the  plurality  of  Adams  and  their  possi- 
bilities is  understood  according  to  the  explanation 
which  I  have  given  and  that  all  this  is  understood 
according  to  our  manner  of  conceiving  any  order  in 
the  thoughts  or  the  operations  which  we  attribute  to 
God),  enter  naturally  enough  into  the  mind  when 
we  think  a  little  about  this  matter,  and  indeed  can- 
not be  avoided;  and  perhaps  they  have  been  displeas- 
ing to  you,  only  because  you  supposed  that  it  was 
impossible  to  reconcile  the  intrinsic  connection 
which  there  would  be,  with  the  free  decrees  of  God. 
All  that  is  actual  can  be  conceived  as  possible  and 
if  the  actual  Adam  will  have  in  time  a  certain  pos- 
terity we  cannot  deny  this  same  predicate  to  this 
Adam  conceived  as  possible,  inasmuch  as  you  grant 
that  God  sees  in  him  all  these  predicates  when 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          131 

he  determines  to  create  him.  They  therefore  per- 
tain to  him.  And  I  do  not  see  how  what  you  say 
regarding  the  reality  of  possibles  could  be  contrary 
to  it.  In  order  to  call  anything  possible  it  is  enough 
that  we  are  able  to  form  a  notion  of  it  when  it  is 
only  in  the  divine  understanding,  which  is,  so  to 
speak,  the  region  of  possible  realities.  Thus,  in 
speaking  of  possibles,  I  am  satisfied  if  veritable 
propositions  can  be  formed  concerning  them.  Just 
as  we  might  judge,  for  example,  that  a  perfect 
square  does  not  imply  contradiction,  although  there 
has  never  been  a  perfect  square  in  the  world,  and  if 
one  tried  to  reject  absolutely  these  pure  possibles 
he  would  destroy  contingency  and  liberty.  •  For  if 
there  was  nothing  possible  except  what  God  has 
actually  created,  whatever  God  created  would  be 
necessary  and  God,  desiring  to  create  anything 
would  be  able  to  create  that  alone  without  having 
any  freedom  of  choice. 

All  this  makes  me  hope  (after  the  explanations 
which  I  have  given  and  for  which  I  have  always 
added  reasons  so  that  you  might  see  that  these  were 
not  evasions  contrived  to  elude  your  objections), 
that  at  the  end  your  thoughts  will  not  be  so  far 
removed  from  mine  as  they  appeared  to  be  at  first. 
You  approve  the  inter-connection  of  God's  resolu- 
tions; you  recognize  that  my  principal  proposition 
is  certain  in  the  sense  which  1  have  given  to  it  in 
my  reply;  you  have  doubted  only  whether  I  made 
the  connection  independent  of  the  free  decrees  of 
God,  and  this  with  good  reason  you  found  hard  to 
understand.  But  I  have  shown  that  the  connection 
does  depend  in  my  opinion  upon  the  decree  and 
that  it  is  not  necessary,  although  it  is  intrinsic. 


I3«  CORRESPONDENCE. 

You  have  insisted  upon  the  difficulties  which  there 
would  be  in  saying,  "If  I  do  not  make  the  journey, 
which  I  am  about  to  make,  I  will  not  be  myself,"  and 
I  have  explained  how  one  might  either  say  it  or  not. 
Finally,  I  have  given  a  decisive  reason  which,  in  my 
opinion,  takes  the  place  of  a  demonstration;  this 
is,  that  always  in  every  affirmative  proposition 
whether  veritable,  necessary  or  contingent,  univer- 
sal or  singular,  the  concept  of  the  predicate  is  com- 
prised in  some  sort  in  that  of  the  subject.  Either 
the  predicate  is  in  the  subject  or  else  I  do  not  know 
what  truth  is. 

Now,  I  do  not  ask  for  any. more  connection  here 
than  what  is  found  a  parte  rei  between  the  terms  of 
a  true  proposition,  and  it  is  only  in  this  sense  that  I 
say  that  the  concept  of  an  individual  substance 
involves  all  of  its  changes  and  all  its  relations,  even 
those  which  are  commonly  called  extrinsic  (that  is 
to  say,  which  pertain  to  it  only  by  virtue  of  the  gen- 
eral inter-connection  of  things,  and  in  so  far  as  it 
expresses  the  whole  universe  in  its  own  way), 
since  "there  must  always  be  some  foundation  for 
the  connection  of  the  terms  of  a  proposition  and 
this  is  found  in  their  concepts."  This  is  my  funda- 
mental principle,  which  I  think  all  philosophers 
ought  to  agree  to,  and  one  of  whose  corollaries  is 
that  commonly  accepted  axiom:  that  nothing  hap- 
pens without  a  reason  which  can  be  given  why  the 
thing  turned  out  so  rather  than  otherwise.  This 
reason,  however,  often  produces  its  effects  without 
necessitation.  A  perfect  indifference  is  a  chimer- 
ical or  incomplete  supposition.  It  has  seemed  that 
from  the  principle  above  mentioned  I  draw  surpris- 
ing consequences  but  the  surprise  is  only  because 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          133 

people  are  not  sufficiently  in  the  habit  of  following 
out  perfectly  evident  lines  of  thought. 

The  proposition  which  was  the  occasion  of  all  this 
discussion  is  very  important  and  should  be  clearly 
established,  for  from  it  follows  that  every  indi- 
vidual substance  expresses  the  whole  universe 
according  to  its  way  and  under  a  certain  aspect,  or, 
so  to  speak,  according  to  the  point  of  view  from 
which  it  is  regarded;  and  that  a  succeeding  condi- 
tion is  a  consequence,  whether  free  or  contingent,  of 
its  preceding  state  as  though  only  God  and  itself 
were  in  the  world.  Thus  every  individual  substance 
or  complete  being  is,  as  it  were,  a  world  apart,  inde- 
pendent of  everything  else  excepting  God.  There 
is  no  argument  so  cogent  not  only  in  demonstrating, 
the  indestructibility  of  the  soul,  but  also  in  showing 
that  it  always  preserves  in  its  nature  traces  of  all 
its  preceding  states  with  a  practical  remembrance 
which  ca.n  always  be  aroused,  since  it  has  the  con- 
sciousness of  or  knows  in  itself  what  each  one  calls 
his  me.  This  renders  it  open  to  moral  qualities,  to 
chastisement  and  to  recompense  even  after  this  life, 
for  immortality  without  remembrance  would  be  of 
no  value.  This  independence  however  does  not 
prevent  the  inter-activity  of  substances  among  them- 
selves, for,  as  all  created  substances  are  a  continual 
production  of  the  same  sovereign  Being  according  to 
the  same  designs  and  express  the  same  universe  or  the 
same  phenomena,  they  agree  with  one  another 
exactly;  and  this  enables  us  to  say  that  one  acts 
upon  another  because  the  one  expresses  more  dis- 
tinctly than  the  other  the  cause  or  reason  for  the 
changes, — somewhat  as  we  attribute  motion  rather 
to  a  ship  than  to  the  whole  sea;  and  this  with 


134  CORRESPONDENCE. 

reason,  although,  if  we  should  speak  abstractly, 
another  hypothesis  of  motion  could  be  maintained, 
that  is  to  say,  the  motion  in  itself  and  abstracted 
from  the  cause  could  be  considered  as  something 
relative.  It  is  thus,  it  seems  to  me,  that  the  inter- 
activities of  created  substances  among  themselves 
must  be  understood,  and  not  as  though  there  were  a 
real  physical  influence  or  dependence.  The  latter 
idea  can  never  be  distinctly  conceived  of.  This  is 
why,  when  the  question  of  the  union  of  the  soul  and 
the  body,  or  of  action  and  of  passion  of  one  spirit 
with  regard  to  another  created  thing,  comes  into 
question,  many  have  felt  obliged  to  grant  that  their 
immediate  influence  one  upon  another  is  inconceiv- 
able. Nevertheless,  the  hypothesis  of  occasional 
causes  is  not  satisfactory,  it  seems  to  me,  to  a  philos- 
opher, because  it  introduces  a  sort  of  continuous 
miracle  as  though  God  at  every  moment  was  changing 
the  laws  of  bodies  on  the  occasions  when  minds  had 
thoughts,  or  was  changing  the  regular  course  of  the 
thinking  of  the  soul  by  exciting  in  it  other  thoughts 
on  the  occasion  of  a  bodily  movement;  and  in  general 
as  though  God  was  interfering  otherwise  for  the  ordi- 
nary events  of  life  than  in  preserving  each  substance 
in  its  course  and  in  the  laws  established  for  it. 
Only  the  hypothesis  of  the  concomitance  or  the 
agreement  of  substances  among  themselves  there- 
fore is  able  to  explain  these  things  in  a  manner 
wholly  conceivable  and  worthy  of  God.  And  as  this 
hypothesis  alone  is  demonstrative  and  inevitable  in 
my  opinion,  according  to  the  proposition  which  we 
have  just  established,  it  seems  also  that  it  agrees 
better  with  the  freedom  of  reasonable  creatures  than 
the  hypothesis  of  impressions  or  of  occasional 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          135 

causes.  God  created  the  soul  from  the  very  start  in 
such  a  manner  that  for  the  ordinary  events  it  has  no 
need  of  these  interventions,  and  whatever  happens 
to  the  soul  comes  from  its  own  being,  without  any 
necessity,  on  its  part,  of  accommodation  in  the 
sequence  of  events  to  the  body,  any  more  than  there 
is  of  the  body's  accommodating  itself  to  the  soul. 
Each  one  follows  its  laws,  the  one  acts  freely,  the 
other  without  choice,  and  they  accord  with  one 
another  in  the  same  phenomena.  The  soul  is  never- 
theless the  form  of  its  body,  because  it  expresses 
the  phenomena  of  all  other  bodies  according  to  their 
relation  to  its  own. 

It  may  be  surprising,  perhaps,  that  I  deny  the 
action  of  one  corporeal  substance  upon  another, 
when  this  seems  so  evident,  but,  besides  the  fact  that 
others  have  already  done  this,  we  must  also  con- 
sider that  it  is  rather  a  play  of  the  imagination  than 
a  distinct  conception.  If  the  body  is  a  substance 
and  not  a  mere  phenomenon,  like  a  rainbow,  nor  a 
being,  brought  together  by  accident  or  by  accumula- 
tion, like  a  pile  of  stones,  its  essence  cannot  consist 
in  extension  and  we  must  necessarily  conceive  of 
something  which  is  called  substantial  form  and 
which  corresponds  in  some  sort  to  the  soul.  I  have 
been  convinced  of  this,  as  it  were,  in  spite  of  myself, 
after  having  held  a  very  different  opinion  before. 
But,  however  much  I  may  approve  of  the  School- 
men in  this  general  and,  so  to  speak,  meta- 
physical accounting  for  the  basis  of  bodies,  I  also 
hold  to  the  corpuscular  theory  as  it  is  used  in  the 
explanation  of  particular  phenomena,  and  for  these 
latter  nothing  is  gained  by  applying  the  terms,  forms 
and  qualities.  Nature  must  always  be  explained 


136  CORRESPONDENCE. 

mathematically  and  mechanically,  provided  it  be 
kept  in  mind  that  the  principles  or  the  laws  of 
rhechanics  and  of  force  do  not  depend  upon  mathe- 
matical extension  alone  but  have  certain  meta- 
physical causes. 

After  all  this  I  think  that  now  the  propositions 
contained  in  the  abstract  which  was  sent  to  you  will 
appear  not  only  more  intelligible  but  perhaps  ten- 
able and  more  important  than  might  have  been 
thought  at  first, 

X 

Leibniz  to  Arnauld. 

Hanover,  July  14,  1686. 
Monsieur: 

I  have  always  had  so  much  esteem  for  your  well- 
known  ability  that  even  when  I  thought  myself  ill- 
treated  by  your  criticism  I  made  the  firm  resolve  to 
say  nothing  but  what  would  express  great  deference 
toward  you;  and  now  you  have  had  the  generosity 
of  making  me  a  restitution  with  interest,  or,  rather, 
with  liberality  —  a  kindness  which  I  shall  cherish 
deeply,  because  it  brings  the  satisfaction  of  think- 
ing that  you  are  well  disposed  toward  me.  When  I 
was  obliged  to  speak  a  little  strongly,  in  order  to 
defend  myself  from  positions  which  you  thought  I 
held,  it  was  because  I  disapproved  of  them  extremely 
and  because  I  thought  so  much  of  your  approbation, 
that  I  was  the  more  sensitive  when  I  saw  you  imput- 
ing them  to  me.  I  hope  that  I  have  been  able  as 
well  to  justify  the  truth  of  my  opinions  as  their 
harmlessness.  This,  however,  is  not  absolutely 
necessary  and  since  error  by  itself  can  do  injury 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          137 

neither  to  piety  nor  to  friendship  I  shall  not  defend 
myself  with  the  same  force;  and  if  in  the  enclosed 
paper  I  have  made  a  reply  to  your  gracious  letter 
where  you  have  pointed  out  very  clearly  and  in  a 
very  instructive  manner  in  what  respect  my  reply 
has  not  yet  satisfied  you,  it  is  not  because  I  pretend 
that  you  will  take  the  time  to  examine  again  my 
reasons,  for  it  is  easy  to  see  that  you  have  more 
important  business  and  these  abstract  questions 
require  leisure.  But  I  have  made  the  reply  so  that 
at  least  you  maybe  able  to  do  so  in  case,  on  account 
of  the  unexpected  consequences  which  can  be 
derived  from  these  abstract  notions,  you  may  wish 
to  divert  yourself  some  day.  I  would  desire  this 
extremely  for  my  own  profit  and  for  the  clearing  up 
of  certain  important  truths  contained  in  my  abstract, 
whose  acceptance  on  your  part  or  at  least  the 
acknowledgement  of  whose  harmlessness,  would  be 
of  great  consequence  to  me.  I  would  wish  it,  I  say, 
if  I  had  not  learned  long  since  to  prefer  the  public 
benefit,  which  is  interested  in  a  wholly  different 
manner  in  the  way  in  which  your  time  is  expended, 
to  my  own  particular  advantage,  which,  however, 
would  not  be  by  any  means  small.  I  have  already 
experienced  this  advantage  from  your  letter  and  I 
know  well  enough  that  there  is  hardly  any  one  in 
the  world  who  can  penetrate  more  ably  into  the 
heart  of  the  matter  and  who  will  be  able  to  shed 
more  light  upon  so  clouded  a  subject.  It  is  with 
difficulty  that  I  speak  of  the  manner  in  which  you 
have  been  willing  to  do  me  justice,  M.,  when  I  asked 
only  that  you  be  gracious  to  me.  I  am  covered  with 
confusion  and  I  say  these  words  only  to  indicate  to 
you  how  sensible  I  am  of  this  generosity  which  is 


138  CORRESPONDENCE. 

very  instructive  to  me;  this  all  the  more  because  it 
is  unusual  and  more  than  unusual  in  a  mind  of  the 
first  rank  Such  a  mind,  reputation  usually  puts  on 
guard,  not  only  against  the  criticism  of  others  but 
also  against  its  own.  It  is  rather  I  who  must  ask 
your  pardon,  and,  as  it  appears  that  you  have  granted 
me  it  in  advance,  I  will  do  my  best  to  acknowledge 
this  goodness,  to  merit  its  effects,  and  to  preserve 
for  myself  always  the  honor  of  your  friendship, 
which  should  be  esteemed  as  so  much  the  more 
precious  because  it  leads  you  to  act  in  accord  with 
such  Christian  and  such  noble  sentiments. 

I  am  not  able  to  let  this  occasion  pass  without 
speaking  to  you  in  regard  to  certain  of  my  medita- 
tions since  1  had  the  honor  of  seeing  you.  Among 
other  things  I  have  made  quite  a  number  of  investi- 
gations into  jurisprudence  and  it  seems  to  me  that 
something  permanent  and  useful  might  be  estab- 
lished, quite  as  much  for  the  sake  of  having  ascer- 
tained laws,  of  which  there  is  a  great  lack  in  Germany 
and  perhaps  also  in  France,  as  also  for  the  establish- 
ment of  short  and  good  forms  of  procedure.  For 
this  purpose  it  is  not  sufficient  to  be  strict  with 
regard  to  the  terms  or  the  established  days  and 
other  conditions,  as  is  the  case  with  the  laws  com- 
piled under  the  code  of  Louis;  for  to  suffer  a  good 
cause  to  be  lost  because  of  formalities,  is  in  juris- 
prudence a  remedy  comparable  to  that  of  a  sur- 
geon who  is  continually  cutting  off  arms  and  legs 
They  say  that  the  King  is  having  work  done  for 
the  reform  of  chicanery,  and  I  think  that  some- 
thing of  importance  might  be  done  along  this  line. 

I   have  also   been    interested    in   the   subject   of 
mines,  because  of  those  which  we  have  in  our  coun- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  139 

try;  and  I  have  frequently  visited  them  by  command 
of  the  Prince.  I  think  I  have  made  several  dis- 
coveries in  regard  to  the  formation,  not  so  much  of 
the  metals  as  of  those  forms  in  which  the  metals  are 
found  and  of  certain  bodies  among  which  they  lie. 
For  example,  I  have  shown  the  manner  of  the  for- 
mation of  slate. 

Besides  this  I  have  gathered  together  memoirs 
and  titles  concerning  the  history  of  Brunswick,  and 
recently  I  read  a  document  regarding  the  boundaries 
of  the  Hildesheim  bishopric  of  the  canonized  Em- 
peror Henry  II.,  where  I  was  surprised  to  find  these 
words,  "for  the  safety  of  his  royal  wife  and  child." 
This  seemed  to  me  to  be  quite  contrary  to  the 
accepted  opinion  which  would  have  us  believe  that 
he  maintained  a  state  of  virginity  toward  his  wife, 
St.  Cunigunde. 

Besides  this  I  have  diverted  myself  frequently 
with  abstract  thoughts  in  metaphysics  and  geometry. 
I  have  discovered  a  new  method  of  tangents,  which 
I  have  had  printed  in  the  Journal  of  Leipsic.  You 
know,  that  Hudde  and  later  De  Sluse  developed  this 
matter  quite  far,  but  there  were  two  things  lacking. 
The  one  was  that  when  the  unknown  term  or 
indeterminate  was  expressed  in  fractions  and  irra- 
tionals, these  had  to  be  eliminated  in  order  to  use 
their  methods,  which  made  the  calculation  assume 
an  extent  and  an  elaborateness  very  awkward  and 
often  unmanageable;  while  my  method  is  not  encum- 
bered at  all  with  fractions  or  irrationals.  This  is 
why  the  English  have  made  so  much  of  it.  The 
other  fault  of  the  method  of  tangents  is  that  it  does 
not  apply  to  the  lines  which  Descartes  calls  mechan- 
ical and  which  I  prefer  to  call  transcendental;  while 


140  CORRESPONDENCE. 

my  method  applies  to  them  just  the  same,  and  I  can 
calculate  the  tangent  of  the  cycloid  or  of  any  other 
line.  I  claim  also  to  give  in  general  the  means 
of  reducing  these  lines  to  calculation,  and  I  hold 
that  they  must  be  received  into  geometry,  whatever 
M.  Descartes  may  say.  My  reason  is  that  there 
are  analytical  problems  which  are  of  no  degree  or 
whose  degree  is  required;  e.g.,  to  cut  an  angle  in  the 
incommensurable  ratio  of  one  straight  line  to  another 
straight  line.  This  problem  is  neither  in  plane  geom- 
metry  nor  in  solid  nor  in  super-solid  geometry,  it  is, 
nevertheless,  a  problem,  and  for  this  reason  I  call  it 
transcendental.  Such  is  also  this  problem:  Solve 
the  following  equation:  2^  +  2  =  30,  where  the  un- 
known term  x  is  found  also  in  the  exponent  and 
the  degree  also  of  an  equation  is  required.  It  is 
easy  to  find  here  that  x  is  equal  to  3  for  3*  +  3  or 
27  +  3  makes  30.  But  it  is  not  always  so  easy  to 
solve  it,  above  all  when  the  exponent  is  not  a 
rational  number;  and  we  must  have  recourse  to  lines 
or  loci  which  are  appropriate  to  the  purpose  and 
which  therefore  must  be  admitted  into  geometry. 
Now  I  show  that  the  lines  which  Descartes  would 
exclude  from  geometry  depend  upon  equations 
which  transcend  algebraic  degrees  but  are  yet  not 
beyond  analysis,  nor  geometry.  I  therefore  call  the 
lines,  which  M.  Descartes  accepts,  algebraic  because 
they  are  of  a  certain  degree  in  an  algebraic  equation. 
The  others  I  call  transcendental.  These  I  reduce  to 
calculations,  and  their  construction  I  show  either 
through  points  or  through  motion;  and,  if  I  might 
venture  to  say,  I  claim  to  advance  analysis  thereby 
ultra  Herculis  columnas. 

Regarding  the  subject  of  metaphysics  I  claim  to 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          141 

advance  by  geometrical  demonstrations,  positing 
only  two  primary  truths;  to  wit,  in  the  first  place, 
the  principle  of  contradiction,  (for  if  two  contradic- 
tories could  be  true  at  the  same  time  all  reasoning 
would  be  useless);  and  secondly,  the  principle  that 
nothing  is  without  reason,  or  that  every  truth  has 
its  proof  a  priori,  drawn  from  the  meaning  of  the 
terms,  although  we  have  not  always  the  power  to 
attain  this  analysis.  I  reduce  all  mechanics  to  a 
single  metaphysical  proposition  and  I  have  several 
important  propositions  in  geometric  form  regarding 
causes  and  effects,  and  the  same  regarding  simili- 
tude by  my  definition  of  which  I  easily  demonstrate 
several  truths  which  Euclid  proves  in  a  roundabout 
way. 

In  addition  I  cannot  approve  the  custom  of  those 
who  have  recourse  to  their  ideas,  when  they  are  at 
the  end  of  their  proofs,  and  who  abuse  the  principle 
that  every  clear  and  distinct  conception  is  good. 
For  I  hold  that  we  must  possess  the  criteria  of  dis- 
tinct knowledge  And  seeing  that  we  often  think 
without  ideas,  employing  in  place  of  the  ideas  in 
question,  characters  whose  signification  we  wrongly 
suppose  ourselves  to  know,  and  thus  form  impos- 
sible chimeras,  therefore  I  hold  that  the  criterion 
of  a  true  idea  is  that  its  possibility  can  be  proved, 
whether  a  priori  in  conceiving  its  cause  or  reason, 
or  a  posteriori  when  experience  enables  us  to  know 
that  it  is  actually  found  in  nature.  This  is  why  I 
consider  definitions  to  be  real  when  it  is  known  that 
the  defined  is  possible;  otherwise  they  are  only 
nominal  and  cannot  be  trusted;  for  if  by  chance  the 
thing  defined  implies  contradictions,  two  contradic- 
tories can  be  deduced  from  the  same  definition.  It 


142  CORRESPONDENCE. 

is  for  this  reason  that  you  had  good  cause  to  insist 
against  Father  Malebranche  that  a  distinction  must 
be  made  between  true  and  false  ideas,  and  that  too 
much  confidence  must  not  be  placed  in  the  imagina- 
tion under  the  pretext  of  a  clear  and  distinct  intel- 
lection. 

I  know  no  one  who  is  better  able  than  yourself  to 
examine  this  class  of  thoughts,  particularly  those 
whose  consequences  lead  into  theology;  few 
people  having  the  necessary  penetration  and  the 
broad  enlightenment  which  is  called  for;  and  few 
people  having  that  fairness  which  you  have  now  dis- 
played toward  me.  I  therefore  pray  God  to 
lengthen  your  life  and  not  to  deprive  us  too  soon  of 
an  ally  whose  like  will  not  be  easily  found  again. 
I  am  yours,  sincerely,  Monsieur, 


XI 


Arnauld  to  Leibniz. 

Sept.  28,  1686. 

I  thought,  M.,  that  I  might  make  use  of  the  lib- 
erty which  you  gave  me  to  take  my  time  in  reply- 
ing to  your  kindness;  and  therefore  I  have  put  it 
off,  until  I  had  completed  a  work  which  I  had  com- 
menced. I  have  been  a  gainer  in  doing  you  justice, 
for  there  was  never  anything  more  honorable  or 
more  gracious  than  the  manner  in  which  you 
received  my  excuses.  So  much  was  not  called  for 
to  make  me  resolve  to  acknowledge  in  good  faith 
that  I  am  satisfied  with  the  manner  in  which  you 
have  explained  what  was  startling  to  me  at  first, 
regarding  the  concept  of  the  individual  nature. 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS.          143 

For  no  man  of  honor  should  have  any  difficulty  in 
accepting  a  truth  as  soon  as  it  is  made  known  to 
him.  I  have  been  above  all  struck  by  this  argu- 
ment, that  in  every  affirmative  true  proposition, 
necessary  or  contingent,  universal  or  singular,  the 
concept  of  the  attributes  is  comprised  in  some  way 
in  that  of  the  subject.  Predicatum  inest  subjecto. 

There  remains  for  me  only  the  difficulty  in  regard 
to  the  possibility  of  things  and  in  regard  to  this  way 
of  conceiving  of  God  as  though  he  had  chosen  the 
universe,  which  he  created,  out  of  an  infinity  of  other 
possible  universes  which  he  saw  at  the  same  time 
and  which  he  did  not  choose  to  create.  But  as  this 
has  nothing  to  do  properly  with  the  concept  of  the 
individual  nature,  and  as  I  should  have  to  meditate 
at  too  great  length  in  order  to  make  clear  what  I 
think  about  it  or  rather  what  I  find  to  object  to  in 
the  thoughts  of  others,  because  they  do  not  seem  to 
me  to  do  justice  to  God's  power,  you  will  permit  me 
to  pass  over  this  subject. 

I  would  prefer  to  ask  you  to  clear  up  two  thfngs 
which  I  find  in  your  last  letter.  They  seem  to  me 
important,  but  I  do  not  understand  them  very 
well. 

The  first  is  as  to  what  you  mean  by  "the  hypoth- 
esis of  the  concomitance  and  of  the  agreement  of 
substances  among  themselves."  You  claim  that  by 
this  means,  that  which  happens  in  the  union  of  the 
soul  and  the  body  and  in  the  action  or  the  passion 
of  a  mind  with  respect  to  any  other  created  thing, 
can  be  explained.  I  cannot  understand  what  you 
say  in  explaining  this  thought,  which,  according  to 
you,  agrees  neither  with  those  who  think  that  the 
soul  acts  physically  upon  the  body  and  the  body 


144  CORRESPONDENCE. 

upon  the  soul,  nor  with  those  who  think  that  God 
alone  is  the  physical  cause  of  these  effects,  and  that 
the  soul  and  the  body  are  only  the  occasional 
causes.  You  say,  "God  created  the  soul  in  such  a 
way  that  for  the  ordinary  events  it  has  no  need  of 
these  changes,  and  that  which  happens  to  the  soul 
arises  from  its  own  being  without  its  having  to 
agree  with  the  body  in  what  results,  any  more  than 
the  body  does  with  the  soul.  Each  one  follows  its 
laws.  The  one  acting  with  freedom  and  the  other 
without  choice,  they  fit  in  together,  one  with 
another,  in  the  same  phenomenon."  Examples 
will  enable  you  to  make  your  thought  clearer:  some 
one  wounds  my  arm.  With  regard  to  my  body,  this 
is  only  a  bodily  motion  but  my  soul  at  once  has  a 
feeling  of  pain  which  it  would  not  have  if  this  had 
not  happened  to  my  arm.  The  question  is,  what  is 
the  cause  of  this  pain?  You  deny  that  my  body  has 
acted  upon  my  soul,  and  that  God,  on  the  occasion 
of  this  which  happened  to  my  arm,  immediately 
produced  in  my  soul  the  feeling  of  pain.  It  must 
be,  therefore,  that  you  think  that  it  is  the  soul 
which  has  formed  this  feeling  in  itself  and  this  must 
be  what  you  mean  when  you  say  that,  "What  hap- 
pens in  the  soul  on  the  occasioning  of  the  body 
arises  from  its  own  being."  St.  Augustine  was  of 
this  opinion  because  he  thought  that  bodily  pain 
was  nothing  else  than  the  grief  which  the  soul  had 
when  its  body  was  ill-affected.  But  what  reply  can 
be  made  to  those  who  object  that  the  soul  must 
therefore  have  known  that  its  body  was  ill-affected 
before  it  could  become  sorrowful,  while  in  fact  it 
seems  to  be  the  pain  which  informs  the  soul  that 
the  body  is  injured. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  145 

Let  us  take  another  example  where  the  body  has 
some  movement  on  the  occasioning  of  the  soul.  If 
I  wish  to  take  off  my  hat,  I  lift  my  arm  to  my  head 
This  movement  of  my  arm  upward  is  not  at  all  in 
line  with  the  ordinary  laws  of  motion.  What  then 
is  its  cause?  It  is  because  the  spirits,  having 
entered  into  certain  nerves,  have  stimulated  them. 
But  these  spirits  have  not  been  through  their 
own  power  determined  to  enter  into  these  nerves. 
They  had  not  given  to  themselves  the  movements 
which  cause  them  to  enter  into  these  nerves.  What 
has  given  it  to  them  then?  Is  it  God,  who  has  done 
it  on  the  occasion  of  my  wishing  to  lift  my  arm? 
This  is  what  the  partisans  of  occasional  causes  say. 
It  seems  that  you  do  not  approve  of  their  position. 
It  must,  therefore,  be  our  soul  itself,  but  this  again 
it  seems  that  you  will  not  grant,  for  this  would  be  to 
act  physically  upon  the  body;  and  you  appear  to 
deny  that  a  substance  can  act  physically  upon 
another. 

The  second  thing  upon  which  .1  should  like  to  be 
enlightened  is  your  statement,  "In  order  that  the 
body  or  matter  should  not  be  a  simple  phenomenon, 
like  a  rainbow,  nor  a  being  brought  together  by  acci- 
dent or  by  an  accumulation,  like  a  pile  of  stones,  it 
must  not  consist  merely  in  extension,  and  there 
must  needs  be  something  which  is  called  the  sub- 
stantial form  and  which  corresponds  in  some  sort 
to  what  is  called  the  soul."  There  are  a  good  many 
things  to  ask  upon  this  point. 

ist.  Our  body  and  our  soul  are  two  substances 
really  distinct.  Now,  if  we  put  into  the  body  a 
substantial  form  aside  from  this  extension,  we  can- 
not imagine  how  there  should  be  two  distinct 


146  CORRESPONDENCE. 

substances,  we  cannot  see  therefore  that  this  sub- 
stantial form  has  any  relation  to  what  we  call  our 
soul. 

2nd.  This  substantial  form  of  the  body  must  be 
either  extended  and  divisible  or  not-extended  and 
indivisible.  If  we  should  say  the  latter,  it  would 
seem  to  be  as  indestructible  as  is  our  soul;  and  if  we 
should  say  the  former,  it  would  seem  that  nothing 
would  be  gained  toward  making  the  body  a  nnum 
per  se,  any  more  than  if  it  consisted  only  in  exten- 
sion. For  it  is  the  divisibility  of  extension  into 
an  infinity  of  parts  which  presents  the  difficulty  of 
conceiving  it  as  a  unit.  This  substantial  form  there- 
fore would  not  remedy  this  difficulty  at  all  so  long 
as  it  also  is  divisible  like  extension  itself. 

3rd.  Is  it  the  substantial  form  of  a  block  of  mar- 
ble which  makes  it  one?  If  this  is  so,  what  becomes 
of  that  substantial  form  when  it  ceases  to  become 
one,  after  it  has  been  cut  in  two?  Is  it  annihilated, 
or  does  it  become  two?  The  first  is  inconceivable, 
if  this  substantial  form  is  not  a  mere  manner  of 
being,  but  is  a  substance;  and  it  cannot  be  said  that 
it  is  a  manner  of  being  or  a  mode,  because  then  the 
substance,  of  which  this  form  would  be  the  mode, 
would  be  an  extension.  This  apparently  is  not  your 
thought.  And  if  this  substantial  form  should  be- 
come two  instead  of  one,  why  would  not  the  same 
be  said  of  the  extended  alone  without  this  substan- 
tial form? 

4th.  Do  you  give  to  extension  a  general  sub- 
stantial form  such  as  has  been  admitted  by  certain 
Schoolmen  who  have  called  it  formam  corporeitatis? 
Or  do  you  wish  that  there  should  be  as  many  differ- 
ent substantial  forms  as  there  are  different  bodies 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          147 

and  are  these  different  in  kind  when  the  bodies  are 
different  in  kind? 

5th.  In  what  do  you  put  the  unity  which  is 
attributed  to  the  earth,  to  the  sun,  or  to  the  moon, 
when  we  say  that  there  is  only  one  earth  which  we 
inhabit,  one  sun  which  lightens  us,  only  one  moon 
which  turns  about  the  earth  in  so  many  days?  Do 
you  think  that  this  earth,  for  example,  made  up  of 
so  many  heterogeneous  parts  must  necessarily  have 
a  substantial  form  which  is  appropriate  to  it  and 
which  gives  to  it  this  unity?  It  does  not  seem  that 
you  believe  this.  I  should  say  the  same  thing  of  a 
tree,  of  a  horse,  and  still  further  I  would  instance 
mixtures;  for  example,  milk  is  composed  of  the 
serum,  of  the  cream,  and  of  the  portion  which  hard- 
ens. Are  there  here  three  substantial  forms,  or  is 
there  only  one? 

6th.  Finally,  it  will  be  said  that  it  is  not  worthy 
of  a  philosopher  to  admit  entities  of  which  there  are 
no  clear  distinct  ideas;  and  there  are  no  such  clear 
and  distinct  ideas  of  these  substantial  forms.  And 
furthermore  even,  you  do  not  let  them  be  proved  by 
their  effects,  since  you  acknowledge  that  it  is  by  a 
corpuscular  philosophy  that  all  the  particular 
phenomenon  of  nature  should  be  explained,  and  that 
there  is  no  advantage  in  bringing  up  these  forms. 

7th.  The  Cartesians  in  order  to  find  unity  in 
bodies  have  denied  that  matter  was  divisible  to 
infinity  and  they  have  held  that  indivisible  atoms 
must  be  accepted;  but  I  think  that  you  do  not  share 
their  opinion. 

I  have  examined  your  little  brochure  and  I  find  it 
very  subtle,  but  take  care  lest  the  Cartesians  should 
reply  that  it  brings  nothing  up  against  their  position, 


148  CORRESPONDENCE. 

because  you  p'osit  something  which  they  think  false 
— namely,  that  a  stone,  in  descending,  gives  to  its 
own  self  this  greater  velocity  which  it  acquires  as  it 
descends.  They  will  say  that  this  acceleration 
comes  from  the  corpuscles,  which,  in  rising,  cause 
everything  that  they  find  in  their  way  to  descend 
and  impart  to  them  a  part  of  the  motion  which  they 
had;  and  therefore  there  is  no  cause  for  surprise  if 
the  body  B,  four  times  the  weight  of  A,  has  more 
motion  when  it  has  fallen  one  foot  than  the  body  A 
when  it  has  fallen  four  feet,  because  the  corpuscles 
which  have  pressed  upon  B  have  communicated  to 
it  a  motion  proportioned  to  its  mass  and  those  which 
have  pressed  upon  A,  in  proportion  to  its  mass.  I 
do  not  assure  you  that  this  reply  will  be  valid,  but  I 
think  at  least  that  you  ought  to  see  if  there  be 
anything  in  it.  I  shall  be  very  glad  to  know  what 
the  Cartesians  have  said  to  your  brochure. 

I  do  not  know  whether  you  have  examined  what 
M.  Descartes  says  in  his  letters  in  regard  to  the  gen- 
eral principle  of  mechanics.  It  seems  to  me  that 
when  he  wishes  to  show  why  the  same  force  can  lift 
by  means  of  a  machine  twice  or  four  times  as  much 
as  what  it  can  lift  without  a  machine,  he  declares 
that  he  has  not  taken  into  consideration  the  velocity. 
My  recollection  about  it,  however,  is  very,  confused, 
for  I  have  gone  into  those  things  only  from  time  to 
time  and  at  odd  moments,  and  it  is  more  than 
twenty  years  since  I  have  seen  any  of  those  books. 

I  do  not  wish  you,  M.,  to  turn  away  from  any  of 
your  occupations  however  important,  in  order  to 
reply  to  the  two  objections  which  I  have  brought 
forward.  You  may  do  as  you  please  about  them  and 
at  your  leisure. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         149 

I  should  like  very  much  to  know  if  you  have  not 
given  the  finishing  touches  to  the  two  machines 
which  you  invented  while  at  Paris.  The  one  in 
the  province  of  arithmetic  seemed  to  be  much  more 
perfect  than  that  of  M.  Pascal,  and  the  other  was 
an  absolutely  correct  watch. 

I  am  yours  devotedly, 


XII 

Count  Ernst  von  Hessen-Rheinfels  to  Leibniz. 

Rheinfels,  21/31,  Oct.,  1686. 
Monsieur: 

I  enclose  herewith  a  letter  from  M.  Arnauld, 
which,  by  some  carelessness  of  mine,  has  been  here 
over  two  weeks.  On  account  of  occupation  in 
other  business  1  have  not  read  it,  and  besides  such 
matters  are  too  remote  and  speculative  for  me.  I 
send  you  also  four  other  writings  that  you  may  be 
interested  in,  and  remain, 

Yours  very  affectionately, 

E. 

XIII 

Draft  of  the  letter  of  Nov.  28-Dec.  8  to  Arnauld. 

The  hypothesis  of  concomitance  is  a  consequence 
of  the  conception  which  I  have  of  substance,  for,  in 
my  opinion,  the  individual  concept  of  a  substance 
involves  all  that  will  ever  happen  to  it,  and  it  is  in 
this  that  complete  beings  differ  from  those  which 
are  not  complete.  Now,  since  the  soul  is  an  indi- 
vidual substance  it  must  be  that  its  concept,  idea, 


150  CORRESPONDENCE. 

essence  or  nature  involves  all  that  will  happen  to  it, 
and  God,  who  sees  it  perfectly,  sees  there  what  it 
will  do  or  endure  forever  and  all  the  thoughts  which 
it  will  have.  Therefore,  since  our  ideas  are  only 
the  consequences  of  the  nature  of  the  soul  and  are 
born  in  it  by  virtue  of  its  concept,  it  is  useless  to  ask 
regarding  the  influence  of  another  particular  sub- 
stance upon  it.  This  aside  from  the  fact  that  this 
influence  would  be  absolutely  inexplicable.  It  is 
true  that  certain  thoughts  come  to  us  when  there  are 
certain  bodily  movements  and  that  certain  bodily 
movements  take  place  when  we  have  certain 
thoughts,  but  this  is  because  each  substance  ex- 
presses the  whole  universe  in  its  fashion  and  this 
expression  of  the  universe  which  brings  about  a 
movement  in  the  body  is  perhaps  a  pain  in  regard 
to  the  soul.  It  is  customary  to  attribute  the  action 
to  that  substance  whose  expression  is  more  distinct 
and  which  is  called  the  cause,  just  as  when  a  body  is 
swimming  in  water  there  are  an  infinity  of  move- 
ments of  the  particles  of  water  in  such  a  way  that 
the  place  which  the  body  leaves  may  always  be  filled 
up  in  the  shortest  way.  This  is  why  we  say  that 
this  body  is  the  cause  of  the  motion,  because  by  its 
means  we  can  explain  clearly  what  happens.  But  if 
we  examine  the  physics  and  the  reality  of  the  motion, 
it  is  quite  as  easy  to  suppose  that  the  body  is  in 
repose  and  that  all  the  rest  is  in  motion  conform- 
ably to  this  hypothesis,  since  every  movement  in 
itself  is  only  relative,  that  is  to  say,  is  a  change 
of  position  which  cannot  be  assigned  to  any  one 
thing  with  mathematical  precision;  but  the  change  is 
attributed  to  that  body  by  means  of  which  the  whole 
is  most  clearly  explained.  In  fact,  if  we  take  all 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          151 

phenomena,  great  or  small,  there  is  only  one  single 
hypothesis  which  serves  to  explain  everything 
clearly.  We  can  therefore  say,  that,  although  this 
body  is  not  an  efficient  physical  cause  of  these 
effects,  its  idea  is  at  least,  so  to  speak,  the  final  cause 
of  them,  or,  if  you  prefer,  a  model  cause*  of  them  in 
the  understanding  of  God;  because,  if  we  wish  to 
ask  what  reality  there  is  in  motion  we  may  imagine 
that  God  desires  expressly  to  produce  all  the 
changes  of  position  in  the  universe  exactly  the 
same  as  that  ship  was  producing  them  while  going 
through  the  water.  Is  it  not  true  that  it  happens 
exactly  in  the  same  way,  for  it  is  not  possible  to 
assign  any  real  difference?  If  we  speak  with  meta- 
physical precision  there  is  no  more  reason  for  say- 
ing that  the  ship  presses  upon  the  water  in  order  to 
make  that  large  number  of  circular  movements 
because  of  which  the  water  takes  the  place  of  the 
ship,  than  to  say  that  the  water  itself  exerts  pressure 
to  make  all  these  circles  and  that  it  therefore  causes 
the  ship  to  move  conformably.  Unless  we  say,  how- 
ever, that  God  expressly  desired  to  produce  such  a 
great  number  of  movements  so  well  fitted  together, 
we  do  not  give  any  real  cause  for  it,  and  as  it  is  not 
reasonable  to  have  recourse  to  divine  activity  for 
explaining  a  particular  detail,  we  have  recourse  to 
the  ship,  notwithstanding  the  fact  that,  in  the  last 
analysis,  the  agreement  of  all  the  phenomena  of 
different  substances  comes  about  only  because  they 
are  productions  of  the  same  cause,  that  is  to  say, 
of  God.  Therefore,  each  individual  substance  ex- 
presses the  resolves  which  God  made  in  regard  to 
the  whole  universe.  It  is  therefore  for  the  same 

*Cause  e.vemplaire  in  the  original. 


152  CORRESPONDENCE. 

reason  that  pain  is  attributed  to  changes  in  the 
body,  because  thus  we  reach  something  distinct  and 
this  is  enough  for  us  to  produce  the  phenomena  or 
to  prevent  them.  In  order  not  to  advance  anything 
that  is  unnecessary,  however,  I  say  that  we  only 
think,  and  also  that  we  produce  only  thoughts,  and 
that  the  phenomena  are  only  thoughts.  As,  how- 
ever, all  our  thoughts  are  not  effective  and  do  not 
serve  to  produce  for  us  others  of  a  certain  nature, 
and  since  it  is  impossible  for  us  to  work  out  the 
mystery  of  the  universal  connection  between 
phenomena,  we  must  pay  attention  by  means  of 
experience  to  those  which  have  produced  thoughts 
before,  and  this  is  the  way  the  senses  do  and  this  is 
what  is  called  external  action,  outside  of  us. 

The  hypothesis  of  the  concomitance  or  of  the 
agreement  of  substances  among  themselves,  follows 
from  what  I  have  said  regarding  each  individual 
substance:  that  it  involves,  forever,  all  the  acci- 
dents that  will  happen  to  it  and  that  it  expresses 
the  whole  universe  in  its  manner.  Thus  whatever 
is  expressed  in  the  body  by  a  movement  .or  by  a 
change  of  position,  is  perhaps  expressed  in  the  soul 
by  a  sense  of  pain.  •  Since  pains  are  only  thoughts, 
we  must  not  be  surprised  if  they  are  the  conse- 
quences of  a  substance  whose  nature  it  is  to  think. 
If  it  happens  constantly  that  certain  thoughts  are 
joined  to  certain  movements,  this  is  because  God 
has  created  from  the  very  start  all  substances  in 
such  away  that  in  the  sequence,  all  their  phenomena 
shall  correspond  without  any  need  for  a  mutual 
physical  influence.  This  latter  does  not  even 
appear  explicable.  Perhaps  M.  Descartes  would 
rather  have  accepted  this  concomitance  than  the 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          153 

hypothesis  of  occasional  causes,  for  so  far  as  I 
know,  he  has  never  expressed  himself  upon  the 
matter.  I  am  pleasantly  surprised,  M.,  that  St. 
Augustine,  as  you  say,  already  held  some  such  view, 
when  he  maintained  that  pain  is  nothing  else  than 
the  grief  which  the  soul  has  when  its  body  is  ill  dis- 
posed. This  great  man  surely  thought  far  into 
things.  The  soul,  however,  feels  that  its  body  is  ill 
disposed,  not  through  an  influence  of  the  body  upon 
the  soul,  nor  by  a  particular  intervention  of  God  who 
carries  the  information,  but  because  it  is  the  nature 
of  the  soul  to  express  whatever  happens  in  the 
body,  having  been  created  from  the  start  in  such  a 
way  that  the  sequence  of  its  thoughts  will  agree 
with  the  sequence  of  the  movements.  The  same  can 
be  said  of  the  motion  of  my  hand  upward.  It  will 
be  asked  what  it  is  that  influences  the  spirits  to  enter 
into  the  nerves  of  a  certain  material;  1  reply  that  it 
is  as  much  the  impressions  made  by  the  objects,  in 
virtue  of  the  ordinary  laws  of  motion,  as  it  is  the  dis- 
position of  the  spirits  or  even  of  the  nerves.  By 
the  general  inter-agreement  of  things,  however,  all 
these  dispositions  happen  only  when  there  is  at  the 
same  time  in  the  soul  the  will  to  which  we  have 
been  accustomed  to  attribute  the  operation.  Thus, 
the  souls  change  nothing  in  the  ordering  of  the 
body  nor  do  the  bodies  effect  changes  in  the  order- 
ing of  the  souls  (and  it  is  for  this  reason  that  forms 
should  not  be  employed  to  explain  the  phenomena  of 
nature).  One  soul  changes  nothing  in  the  sequence 
of  thought  of  another  soul,  and  in  general  one  par- 
ticular substance  has  no  physical  influence  upon 
another;  such  influence  would  besides  be  useless 
since  each  substance  is  a  complete  being  which 


154  CORRESPONDENCE. 

suffices  of  itself  to  determine  by  virtue  of  its  own 
nature  all  that  must  happen  to  it.  Nevertheless, 
one  has  good  reason  to  say  that  my  will  is  the  cause 
of  this  movement  of  my  arm  and  that  an  interrup- 
tion in  the  continuity  of  the  matter  of  my  body  is  the 
cause  of  the  pain,  for  the  one  expresses  distinctly 
what  the  other  expresses  more  confusedly  and  the 
action  should  be  attributed  to  the  substance  whose 
expression  is  most  distinct.  The  same  can  be  said 
practically  where  phenomena  are  produced.  If  it  is 
not  a  physical  cause,  we  can  say  that  it  is  a  final 
cause  or  better  a  model  cause,  that  is  to  say,  that  the 
idea  in  the  understanding  of  God  has  contributed  to 
God's  resolve  in  regard  to  this  particularity,  when 
the  determination  regarding  the  universal  sequence 
of  things  was  being  made. 

The  second  difficulty  is  incomparably  greater 
regarding  the  substantial  forms  and  the  souls  of 
bodies,  and  I  grant  that  I  am  not  myself  satisfied  in 
regard  to  it.  First  of  all,  we  must  maintain  that 
the  bodies  are  substances  and  not  merely  true 
phenomena  like  the  rainbow,  but,  on  the  other  hand, 
even  if  this  were  granted,  it  might  be  inferred,  I 
think,  that  the  corporeal  substance  consists  neither 
in  extension  nor  in  divisibility  for  it  will  be  granted 
that  two  bodies  distant  from  each  other,  for  exam- 
ple, two  triangles  are' not  really  one  substance;  sup- 
pose now  that  they  come  together  to  compose  a 
square,  does  the  mere  contact  make  them  one  sub- 
stance? I  do  not  think  so.  Now,  every  extended 
mass  may  be  considered  as  a  composite  of  two  or  of 
a  thousand  others,  and  the  only  extension  there  is,  is 
that  by  contact.  Consequently,  we  shall  never  find 
a  body  of  which  we  can  say  that  it  is  really  one 


LEIBNIZ.       ARNAULD.        HESSEN-RHEINFELS.          155 

substance;  it  will  always  be  an  aggregate  of  several. 
Or  rather,  it  will  not  be  a  real  being,  because  the 
component  parts  are  subject  to  the  same  difficulty, 
and  we  should  never  reach  a  real  being,  for  the 
beings  which  result  from  an  aggregation  have  only 
as  much  reality  as  there  is  in  their  ingredients. 
Whence  it  follows  that  the  substance  of  a  body,  if  it 
has  one,  must  be  indivisible;  whether  we  call  it 
soul  or  form  makes  no  difference  to  me. 

The  general  conception  of  individual  substance, 
which  seems  to  appeal  to  you,  M.,  evidences  the 
same  thing,  that  extension  is  an  attribute  which  can 
never  constitute  a  complete  being;  no  action  can 
ever  be  derived  from  extension,  and  no  change.  It 
merely  expresses  a  present  state.  Never  does  it 
express  the  future  or  the  past  state  as  the  concep- 
tion of  a  substance  should.  When  two  triangles  are 
joined,  we  cannot  decide  how  this  union  is  made, 
for  this  might  happen  in  several  ways,  and  what- 
ever can  have  several  causes  is  never  a  complete 
being. 

Nevertheless,  I  acknowledge  that  it  is  very  diffi- 
cult to  answer  several  question  which  you  have  put, 
I  think  we  must  say  that  if  bodies  or  substantial 
forms,  for  example,  if  the  beasts  have  souls,  then 
these  souls  are  indivisible.  This  is  also  the  opin- 
ion of  St. Thomas.  Are  these  souls  therefore  inde- 
structible? I  think  they  are,  unless  it  is  possible 
that  in  accordance  with  the  opinion  of  M.  Leeuwen- 
hoeck  every  birth  of  an  animal  is  only  the  transfor- 
mation of  an  animal  already  alive.  There  is 
ground,  moreover,  for  thinking  that  death  is  also 
another  transformation.  The  soul  of  man,  how- 
ever, is  something  more  divine.  It  is  not  only 


156  CORRESPONDENCE. 

indestructible  but  it  always  knows  itself  and  con- 
tinues to  exist  with  self-consciousness.  Regarding 
its  origin,  it  can  be  said  that  God  produced  it  only 
when  this  animated  body,  which  was  in  the  seed, 
determined  itself  to  assume  human  form.  This  brute 
soul,  which  formerly  animated  this  body  before 
the  transformation,  is  annihilated  when  the  reasoning 
soul  takes  its  place;  or  if  God  changes  the  one  into 
the  other  by  giving  to  the  former  a  new  perfection 
by  means  of  an  extraordinary  intervention,  this  is  a 
particular  in  regard  to  which  I  have  not  sufficient 
light. 

I  do  not  know  whether  the  body,  when  the  soul  or 
substantial  part  is  put  aside,  can  be  called  a  sub- 
stance. It  might  very  well  be  a  machine,  an  aggre- 
gation of  several  substances,  of  such  sort  that  if  I 
were  asked  what  I  should  say  regarding  the  forma 
cadaveris  or  regarding  a  block  of  marble,  I  should 
say  that  they  might  perhaps  be  units  by  aggre- 
gation, like  a  pile  of  stones,  but  that  they  are  not 
substances.  The  same  may  be  said  of  the  sun,  of 
the  earth,  of  machines;  and  with  the  exception  of 
man,  there  is  no  body,  of  which  I  can  be  sure  that  it 
is  a  substance  rather  than  an  aggregate  of  several 
substances  or  perhaps  a  phenomenon.  It  seems  to 
me,  however,  certain,  that  if  there  are  corporeal  sub- 
stances, man  is  not  the  only  one,  and  it  appears 
probable  that  beasts  have  souls  although  they  lack 
consciousness. 

Finally,  although  I  grant  that  the  consideration  of 
forms  or  souls  is  useless  in  special  physics,  it  is, 
nevertheless,  important  in  metaphysics.  Just  as 
geometers  pay  no  attention  to  the  composition  of 
the  continuum,  and  physicists  do  not  ask  whether 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          I$7 

one  ball  pushes  another  or  whether  it  is  God  who 
does  this. 

It  would  be  unworthy  of  a  philosopher  to  admit 
these  souls  or  forms  without  reason,  but  without 
them  it  is  not  possible  to  understand  how  bodies 
are  substances. 

XIV 

Leibniz  to  Arnauld. 

Hanover,  Nov.  28-Dec.  8,  1686. 
Monsieur: 

As  I  have  found  something  very  extraordinary  in 
the  franknes^  and  in  the  sincerity  with  which  you 
accepted  certain  arguments  which  I  employed,  I 
cannot  avoid  recognizing  it  and  wondering  at  it.  1 
was  quite  confident  that  the  argument,  based  upon 
the  general  nature  of  propositions,  would  make 
some  impression  upon  your  mind,  but  I  confess  at 
the  same  time  that  there  are  few  people  able  to 
enjoy  truths  so  abstract  whose  cogency,  perhaps,  no 
one  else  would  have  been  able  to  see  so  easily.  I 
should  like  to  be  instructed  by  your  meditations 
regarding  the  possibilities  of  things.  They  would 
certainly  be  profound  and  important,  inasmuch  as 
they  would  have  to  deal  with  those  possibilities  in  a 
manner  that  might  be  worthy  of  God.  But  this  will 
be  at  your  convenience.  As  regards  the  two  diffi- 
culties which  you  have  found  in  my  letter,  the  one 
regarding  the  hypothesis  of  the  concomitance  or  of 
the  agreement  of  substances  among  themselves,  the 
other  regarding  the  nature  of  the  forms  of  corporeal 
substances,  I  grant  that  the  difficulties  are  consider- 
able, and  if  I  were  able  to  meet  them  entirely  I 


158  CORRESPONDENCE. 

should  think  myself  able  to  decipher  the  greatest 
secrets  of  universal  nature.  But  est  aliquid  prodire 
tenus. 

As  regards  the  first  I  find  that  you  have  yourself 
sufficiently  explained  the  obscurity  that  you  found 
in  my  statement  concerning  the  hypothesis  of  con- 
comitance, for,  when  the  soul  has  a  feeling  of  pain 
at  the  same  time  that  the  arm  is  injured,  I  think  it 
is  as  you  say,  M.,  that  the  soul  forms  for  itself  this 
pain,  which  is  a  natural  consequence  of  its  condition 
or  of  its  concept.  And  it  is  surprising  that  St. 
Augustine,  as  you  have  remarked,  seems  to  have 
recognized  the  same  thing,  when  he  said  that  the 
pain  which  the  soul  has  in  these  accidents  is  noth- 
ing else  than  a  grief  which  accompanies  the  ill  con- 
dition of  the  body.  In  fact,  this  great  man  has 
very  stable  and  profound  thoughts.  But  it  will  be 
asked,  how  does  the  soul  know  this  ill  condition  of 
the  body?  I  reply  that  it  is  not  by  any  impression 
or  action  of  the  body  upon  the  soul  but  because  the 
nature  of  every  substance  carries  a  general  expres- 
sion of  the  whole  universe  and  because  the  nature 
of  the  soul  bears  more  particularly  a  distincter 
expression  of  that  which  happens  immediately  to 
its  body.  This  is  why  it  is  natural  for  it  to  notice 
and  to  recognize  the  accidents  of  its  body  by  its  own 
accidents.  The  same  is  true  with  regard  to  the 
body  when  it  accommodates  itself  to  the  thoughts 
of  the  soul,  and  when  I  wish  to  raise  my  arm  it  is 
exactly  at  the  very  moment  when  everything  is 
ready  in  the  body  for  this  effect;  in  such  a  way  that 
the  body  moves  in  virtue  of  its  own  laws;  while  it 
happens,  by  the  wonderful  though  unfailing  agree- 
ment of  things  among  themselves,  that  these  laws 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          159 

work  together  exactly  at  the  moment  that  the  will  is 
so  inclined.  God  had  regard  to  this  in  advance  when 
he  formed  his  resolve  in  regard  to  this  sequence  of 
all  the  things  in  the  universe.  All  of  this  is  only 
the  consequence  of  the  concept  of  an  individual 
substance,  which  involves  all  its  phenomena  in  such 
a  way  that  nothing  can  happen  to  its  substance  that 
does  not  come  from  its  own  being,  conformably, 
however,  to  that  which  happens  to  another,  although 
the  one  may  act  freely  and  the  other  without 
choice.  This  agreement  is  one  of  the  best  proofs 
that  can  be  given  of  the  necessity  of  a  substance 
which  shall  be  the  sovereign  cause  of  everything. 

I  should  like  to  be  able  to  explain  as  clearly  and 
decisively  the  other  question  with  regard  to  the 
substantial  forms.  The  first  difficulty  which  you 
point  out,  M.,  is  that  our  souls  and  our  bodies  are 
two  substances  really  distinct;  therefore,  it  seems 
that  one  is  not  the  substantial  form  of  the  other.  I 
reply  that  in  my  opinion  our  body  by  itself,  leaving 
out  of  question  the  soul,  the  physical  body,  can  be 
called  one  substance  only  by  a  misuse  of  terms, 
just  as  a  machine  or  a  pile  of  stones  might  be 
called  one  although  they  are  beings  only  by  accu- 
mulation. The  regular  or  irregular  arrangement 
does  not  constitute  a  substantial  unity.  Aside  from 
this,  the  last  Lateran  council  declares  that  the  soul  is 
veritably  the  substantial  form  of  our  body. 

Regarding  the  second  difficulty  I  agree  that  the 
substantial  form  of  our  body  is  indivisible  and  this 
seems  also  to  be  the  opinion  of  St.  Thomas.  I 
agree,  also,  that  every  substantial  form,  or,  indeed, 
every  substance  is  indestructible  and  also  ingener- 
able,  which  latter  was  also  the  opinion  of  Albertus 


l6o  CORRESPONDENCE. 

Magnus  and  among  the  ancients  of  the  author  of  the 
book  called  De  diaeta,  usually  attributed  to  Hippoc- 
rates. They  can  come  into  being  therefore  only 
by  an  act  of  creation.  I  am  a  good  deal  inclined  to 
believe  that  all  the  births  of  unreasoning  animals, 
which  do  not  deserve  a  new  act  of  creation,  are  only 
transformations  of  another  animal  already  living, 
but  at  times  invisible.  Consider  for  example,  the 
changes  which  happen  to  a  silk-worm  and  other  like 
creatures,  where  nature  has  disclosed  its  secrets  in 
certain  instances  while  it  conceals  them  in  others. 
Thus,  brute  souls  would  have  all  been  created  from 
the  very  beginning  of  the  world,  in  accordance  with 
that  fertility  of  seeds  mentioned  in  Genesis,  but  the 
reasoning  soul  is  created  only  at  the  time  of  the 
formation  of  its  body,  being  entirely  different  from 
the  others  souls  which  we  know  because  it  is  cap- 
able of  reflection  and  imitates  on  a  small  scale  the 
divine  nature. 

Thirdly,  I  think  that  a  block  of  marble  is,  per- 
haps, only  a  mass  of  stones  and  thus  cannot  be 
taken  as  a  single  substance  but  as  an  assembly  of 
many.  For,  supposing  there  are  two  stones,  (for 
example,  the  diamond  of  the  Grand  Duke  and  that 
of  the  Great  Mogul),  the  same  collective  name 
could  be  put  for  both  of  them,  and  we  could  say  that 
it  is  a  pair  of  diamonds,  although  they  are  very  far 
apart;  but,  we  should  not  say  that  these  two  dia- 
monds compose  one  substance.  Matters  of  greater  or 
less  in  this  case  would  make  no  difference.  They 
might  be  brought  nearer  together,  even  to  touch- 
ing. Yet  they  would  not  be  substantially  one,  and 
if,  after  they  had  touched  they  were  joined  together 
by  some  other  body,  constructed  to  prevent  their 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          l6l 

separation — for  instance,  if  they  were  set  in  the 
same  ring — all  this  would  make  only  what  is  called 
a  unity  by  accident,  for  it  is  as  by  accident  that 
they  are  subjected  to  the  same  motion.  I  hold, 
therefore,  that  a  block  of  marble  is  no  more  a 
thoroughly  single  substance  than  would  be  the 
water  in  a  pond  with  all  the  fish  included,  even 
when  all  the  water  and  all  the  fish  were  frozen;  or 
any  more  than  a  flock  of  sheep,  even  when  the  sheep 
were  tied  together  so  that  they  could  only  walk  in  step 
and  so  that  one  could  not  be  touched  without  pro- 
ducing a  cry  from  all.  There  is  as  much  difference 
between  a  substance  and  such  a  being,  as  there  is 
between  a  man  and  a  community — say  a  people,  an 
army,  a  society  or  college,  which  are  moral  beings, 
yet  they  have  an  imaginary  something  and  depend 
upon  the  fiction  of  our  minds.  Substantial  unity 
calls  for  a  thoroughly  indivisible  being,  naturally 
indestructible  since  its  concept  involves  all  that 
must  happen  to  it.  This  characteristic  cannot  be 
found  either  in  forms  or  in  motions,  both  of  which 
involve  something  imaginary  as  I  could  demon- 
strate. It  can  be  found,  however,  in  a  soul  or  a 
substantial  form,  such  as  is  the  one  called  the  me. 
These  latter  are  the  only  thoroughly  real  beings  as 
the  ancients  recognized  and,  above  all,  Plato,  who 
showed  very  clearly  that  matter  alone  does  not 
suffice  for  forming  a  substance.  Now,  the  me 
above  mentioned  or  whatever  corresponds  to  it,  in 
each  individual  substance  can  neither  be  made  nor 
destroyed  by  the  bringing  together  or  the  separa- 
tion of  the  parts.  Such  juxtapositions  are  wholly 
apart  from  the  constitution  of  a  substance.  I  can- 
not tell  exactly  whether  there  are  other  true  cor- 


l6«  CORRESPONDENCE. 

poreal  substances  beside  those  which  have  life. 
But  souls  serve  to  give  us  a  certain  knowledge  of 
others  at  least  by  analogy. 

All  this  can  contribute  to  clear  up  the  fourth  dif- 
ficulty, for,  without  bothering  with  what  the  School- 
men have  called  formam  corporeitatis,  I  assign  sub- 
stantial forms  to  all  corporeal  substances  that  are 
more  than  mechanically  united. 

But  fifthly,  if  I  am  asked  in  particular  what  I 
should  say  of  the  sun,  the  earth,  the  moon,  of  the 
trees,  and  of  similar  bodies,  and  even  of  the  beasts, 
I  am  not  able  to  say  surely  whether  they  are  ani- 
mated, or  at  least  whether  they  are  substances,  or 
whether  they  are  merely  machines  or  aggregations 
of  several  substances,  but  I  am  able  to  say  that  if 
there  are  no  corporeal  substances  such  as  I  claim,  it 
follows  that  bodies  are  only  true  phenomena  like 
the  rainbow.  For  a  continuum  is  not  only  divis- 
ible to  infinity,  but  every  particle  of  matter  is 
actually  divided  into  other  parts  as  different  among 
themselves  as  were  the  two  diamonds  above  men- 
tioned. And  since  this  could  always  be  continued, 
we  should  never  reach  anything  of  which  we  could 
say,  here  is  really  a  being,  unless  there  were 
found  animated  machines  whose  soul  or  sub- 
stantial form  constituted  the  substantial  unity  inde- 
pendently of  the  external  union  of  contact.  And  if 
there  are  no  substantial  forms,  it  follows  that  with 
the  exception  of  men  there  is  nothing  substantial  in 
the  visible  world. 

Sixthly,  since  the  conception  of  an  individual 
substance  in  general,  which  I  have  given,  is  as  clear 
as  is  the  conception  of  truth,  the  conception  of  cor- 
poreal substance  will  be  clear  also,  and  consequently 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          163 

that  of  substantial  forms.  If,  however,  this  should 
not  be  so,  we  should  be  obliged  to  admit  a  good 
many  things  whose  knowledge  is  not  so  clear  and 
distinct.  I  hold  that  the  conception  of  extension 
is  much  less  clear  and  distinct;  witness  the  remark- 
able difficulties  found  in  the  composition  of  the  con- 
tinuum. And  it  can,  indeed,  be  said  that  there  is  no 
definite  and  precise  form  in  the  body  because  of  the 
actual  subdivision  of  the  parts.  With  infinite  sub- 
division the  body  would  be  doubtless  imaginary  and 
a  mere  appearance,  if  there  was  only  the  material  and 
its  modifications.  Nevertheless,  it  is  useless  to  make 
mention  of  the  unity,  the  concept,  or  the  substantial 
forms  of  bodies  when  it  is  a  question  of  explaining 
the  particular  phenomena  of  nature,  just  as  it  is  use- 
less for  Geometers  to  examine  the  difficulties  of  the 
continuum  when  they  are  at  work  in  solving  some 
problem.  These  things  are  nevertheless  important 
and  worthy  of  consideration  in  their  place;  all  the 
phenomena  of  the  body  can  be  explained  mechanic- 
ally or  by  the  corpuscular  philosophy  in  accor- 
dance with  certain  assumed  mechanical  principles 
without  troubling  oneself  as  to  whether  there  are 
souls  or  not.  In  the  ultimate  analysis  of  the  prin- 
ciples of  physics  and  mechanics,  however,  it  is  found 
that  these  assumed  principles  cannot  be  explained 
solely  by  the  modifications  of  extension,  and  the 
very  nature  of  force  calls  for  something  else. 

Finally,  in  the  seventh  place  I  remember  that  M. 
Cordemoy,  in  his  treatise  on  the  distinction  between 
the  body  and  the  soul,  in  order  to  save  the  substan- 
tial unity  in  the  body,  feels  himself  obliged  to 
assume  atoms  or  indivisible  extended  bodies,  so  as 
to  have  something  permanent  to  constitute  a  simple 


164  CORRESPONDENCE. 

being;  but  you  rightly  concluded,  M.,  that  I  did  not 
share  this  opinion.  It  appears  that  M.  Cordemoy 
made  an  approach  to  the  truth,  but  he  did  not  yet 
see  in  what  the  true  notion  of  a  substance  consisted 
and  this  latter  is  the  key  for  most  important  knowl- 
edge. The  atom,  which  consists  of  only  an  imagined 
mass  with  an  infinite  duration,  an  idea  which  I  hold 
conforms  no  more  to  the  divine  wisdom  than  does 
a  vacuum,  cannot  contain  in  itself  all  its  past 
and  future  states  and  much  less  those  of  the  whole 
universe. 

I  come  to  your  observations  upon  my  objection  to 
the  Cartesian  principle  regarding  the  quantity  of 
motion,  and  I  grant,  M.,  that  the  acceleration  of  a 
body  comes  from  the  impulse  of  some  invisible  fluid 
and  that  it  is  like  a  ship  which  the  wind  causes  to 
go  at  first  very  slowly  and  then  faster;  my  demon- 
stration, however,  is  independent  of  any  hypothesis. 
Without  troubling  myself  at  present  as  to  how  the 
body  has  acquired  the  velocity  which  it  has,  I 
accept  it  such  as  it  is,  and  I  say  that  a  body  weigh- 
ing one  pound,  which  has  a  velocity  of  two  degrees, 
has  twice  as  much  force  as  a  body  weighing  two 
pounds  which  has  a  velocity  of  one  degree,  because 
it  can  raise  the  same  weight  twice  as  high.  I  hold 
that  in  distributing  the  motion  between  bodies 
which  come  into  contact,  regard  must  be  had,  not 
to  the  quantity  of  motion,  as  is  the  case  in  the 
Cartesian  principle,  but  to  the  quantity  of  the  force; 
otherwise,  we  should  obtain  perpetual  motion  in 
mechanics.  For  example,  suppose  that  in  a  square 
LM  a  body  A  goes  along  the  diagonal  lA  2A  to 
strike  two  equal  bodies  B  and  C  at  the  same 
moment  in  such  a  way  that  at  the  moment  of  con- 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS. 


tact  the  three  centers  of  these  three  spheres  are 
found  in  an  isosceles  right  triangle,  the  whole  being 
in  a  horizontal  plane.  Suppose  now  that  the  body 
A  remains  at  rest  after  the  contact  in  the  place  2A, 
and  imparts  all  its  force  to  the  bodies  B  and  C.  In 
this  case  B  would  go  from  iB  to  26,  having  the 
velocity  and  direction  1626,  and  C  from  iC  to  2C, 
with  the  velocity  and  direction  iCzC.  That  is  to 
say,  if  A  takes  one 
second  of  time  to  pass 
with  uniform  motion 
from  lA  to  2A  before 
contact,  then  in  one 
second  after  contact  B 
will  pass  to  26,  and  C 
to  2C.  The  question 
is,  what  is  the  length 
of  1626  or  i  C  2  C, 
which  represent  the 
velocity.  I  say  that 
it  will  be  equal  to  AL  or  AM  sides  of  the  square 
LM,  for  the  bodies,  being  supposed  equal,  the 
forces  would  be  only  as  the  height  from  which  the 
body  would  have  to  descend  in  order  to  acquire 
these  velocities,  that  is  to  say,  as  the  squares  of  the 
velocities.  Now,  the  squares  of  1626  and  iCaC 
taken  together  are  equal  to  the  square  iA2A. 
Hence,  there  is  as  much  force  after  as  before  the 
contact.  But  we  see  that  the  quantity  of  motion 
has  been  augmented;  for,  since  the  bodies  are  equal, 
the  quantity  of  motion  can  be  estimated  by  their 
velocities.  Now,  before  the  contact  this  was  the 
velocity  iA2A  but  after  the  contact  it  is  the 
velocity  iB2B  plus  the  velocity  iC2C;  1626  plus 


l66  CORRESPONDENCE. 

lC2C,  however,  is  greater  than  lA2A;  it  must  needs 
be,  therefore,  that,  according  to  M.  Descartes,  in 
order  to  maintain  the  same  amount  of  motion  the 
body  B  would  go  from  iB  only  to  /3,  or  from  iC 
only  to  K,  in  such  a  way  that  iB/3  or  iGc  shall  each  be 
equal  to  half  I A2A.  In  this  way,  however,  there  will 
be  as  much  force  lost  as  the  two  squares  of  iB/3  and  of 
iGc,  taken  together  are  less  than  the  square  iA2A. 

And,  on  the  other  hand,  I  will  show  that  by 
another  means  force  can  be  gained  through  the  con- 
tact. For,  since  according  to  M.  Descartes,  the 
body  A  with  the  velocity  and  direction  iA2A  gives 
by  hypothesis  to  the  bodies  at  rest  B  and  C 
velocities  and  directions  iB/3  and  iC/c  so  that  it  may 
come  to  rest  in  their  place,  reciprocally  if  these 
bodies  should  return  and  come  in  contact  with  the 
body  A  resting  at  2A  with  the  velocities  and  direc- 
tions fiiB  and  KiC  and  should  come  to  rest  after  the 
contact,  they  would  make  A  move  with  the  velocity 
and  direction  2AiA.  In  this  way,  however,  per- 
petual motion  would  be  inevitably  attained  for,  sup- 
posing that  the  body  B,  weighing  one  pound  with 
the  velocity  ftiB  could  rise  to  the  height  of  one  foot, 
and  C  the  same,  there  would  be  before  the  shock  a 
force  capable  of  lifting  two  pounds  to  the  height  of 
one  foot,  or  one  pound  the  height  of  two  feet,  but, 
after  the  contact  of  iB  and  iC  with  2A  the  body  A 
weighing  one  pound  and  having  a  double  velocity 
(that  is  to  say,  the  velocity  of  2AiA,  double  the 
velocity  of  /?iB  or  of  KiC),  could  lift  one  pound  to 
the  height  of  four  feet,  for  the  height  to  which  the 
bodies  can  rise  by  virtue  of  their  velocities  is  as  the 
squares  of  their  velocities.  If,  therefore,  double  the 
force  can  be  gained,  perpetual  motion  is  completely 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          167 

discovered,  or  it  is  possible  that  force  should  be 
gained  or  lost,  and  principles  are  not  well-based 
when  such  consequences  can  be  derived  from 
them. 

I  found  in  Descartes'  letters  what  you  mentioned 
to  me — namely,  that  he  had  tried  to  avoid  the  con- 
sideration of  velocities  in  formulating  the  reasons 
for  moving  forces  and  had  taken  into  account  only 
the  heights.  If  he  had  remembered  this  when  he 
wrote  his  principles  of  physics  perhaps  he  would 
have  avoided  the  errors  into  which  he  has  fallen 
with  respect  to  the  laws  of  nature,  but  he  happens  to 
have  avoided  the  consideration  of  velocity  there 
where  he  might  have  retained  it,  and  to  have  retained 
it  in  the  case  where  it  could  produce  errors.  For, 
with  regard  to  the  power  which  I  call  dead  (as  when 
a  body  makes  its  first  effort  to  descend  before  it  has 
acquired  any  impetus  from  the  continuance  of  the 
motion),  and  with  regard  to  the  case  when  two 
bodies  are  in  equilibrium  (for  then,  the  first  efforts 
which  the  one  exercises  on  the  other  are  always 
dead),  it  happens  that  the  velocities  are  as  the  dis- 
tances; when,  however,  we  consider  the  absolute 
force  of  bodies  which  have  a  certain  impetuosity 
(and  this  is  necessary  for  establishing  the  laws  of 
motion),  the  calculation  should  be  made  from  the 
cause  or  from  the  effect,  that  is  to  say,  according  to 
the  height  to  which  it  can  rise  by  virtue  of  this 
velocity,  or  according  to  the  height  from  which  it 
must  descend  in  order  to  acquire  this  velocity.  If 
we  should  attempt  to  employ  the  velocity,  we  should 
gain  or  lose  a  great  deal  of  force  without  any  reason 
for  it.  In  place  of  the  height  we  might  suppose  a 
spring  or  any  other  cause  or  effect,  and  the  result 


l68  CORRESPONDENCE. 

would  always  be  the  same;  viz.,  proportional  to  the 
squares  of  the  velocities. 

I  find  in  The  News  of  the  Republic  of  Letters  for 
the  month  of  September,  of  this  year,  that  someone 
named  Abbe  D.  C.,  of  Paris,  whom  I  do  not  know, 
has  replied  to  my  objection.  The  trouble  is  that  he 
seems  not  sufficiently  to  have  thought  over  the 
difficulty.  While  pretending  to  contradict  me 
vehemently  he  grants  me  more  than  I  wish  and  he 
limits  the  Cartesian  principle  to  the  single  case  of 
isochronous  powers  as  he  calls  them,  as  in  the  five 
usual  forms  of  machinery,  and  this  is  entirely 
against  Descartes'  intention.  Besides  this,  he 
thinks  that  the  reason  why  in  the  case  which  I  pro- 
posed one  of  the  bodies  has  quite  as  much  force  as 
the  other  although  it  has  a  smaller  quantity  of 
motion,  is  the  result  of  this  body's  having  fallen  for 
a  longer  period  since  it  has  come  from  a  greater 
height.  If  this  made  any  difference,  the  Cartesian 
principle  which  he  wishes  to  defend  would  be  ruined 
by  that  very  fact.  This  reason,  however,  is  not 
valid,  for  the  two  bodies  can  descend  from  those 
different  heights  in  the  same  time,  according  to  the 
inclination  which  is  given  to  the  planes  along  which 
they  must  descend;  and  my  objection  would  still  be 
entirely  valid.  I  hope,  therefore,  that  my  objec- 
tion maybe  examined  by  a  Cartesian  who  shall  be  a 
Geometer  and  well  versed  in  these  matters. 

Finally,  M.,  as  I  honor  you  infinitely  and  am  very 
much  interested  in  whatever  concerns  you  I  will  be 
delighted  to  learn  from  time  to  time  of  the  state  of 
your  health  and  of  the  works  which  you  have  in 
hand;  whose  value  I  am  proud  to  be  able  to  recog- 
nize. I  am,  with  a  passionate  zeal, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          169 


XV 

Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

[Taken  from  my  letter  of  November,  1686.] 

I  take  the  liberty,  Monseigneur,  to  beg  your  Serene 
Highness  to  have  the  enclosed  sent  to  M.  Arnaud, 
and,  as  it  treats  of  matters  far  from  the  external 
senses  and  dependent  upon  pure  intellection,  which 
are  not  agreeable  to  and  most  frequently  are  looked 
down  upon  by  persons  who  are,  nevertheless,  active 
and  successful  in  the  affairs  of  the  world,  I  will  say 
here  something  in  favor  of  these  meditations;  not 
because  I  am  so  fatuous  as  to  wish  your  Serene  High- 
ness to  amuse  himself  with  them  (this  would  be  as 
unreasonable  as  to  wish  that  the  general  of  an  army 
should  apply  himself  to  algebra,  however  important 
this  science  may  be  to  any  one  who  is  concerned 
with  mathematics),  but  so  that  your  Serene  High- 
ness may  better  estimate  the  purpose  and  the  use  of 
such  thoughts  that  might  appear  unworthy  of  taking 
up  a  man's  time;  especially  since  all  a  man's 
moments  ought  to  be  so  precious  to  him.  As  these 
matters  are  usually  treated  by  the  Schoolmen,  they 
are  only  disputations  and  distinctions  and  plays 
upon  words;  but  there  are  veins  of  gold  among  these 
barren  rocks.  I  think  in  fact  that  thought  is  the 
principal  and  perpetual  function  of  the  soul.  We 
shall  always  think,  but  we  shall  not  always  live  here; 
this  is  why  whatever  renders  us  more  capable  of 
thinking  about  most  perfect  objects  and  in  the  most 
perfect  way  is  what  naturally  contributes  to  our  per- 
fection. Nevertheless,  the  present  state  of  our  life 
compels  us  to  a  great  number  of  confused  thoughts 


170  CORRESPONDENCE. 

which  do  not  add  to  our  perfection,  such  is  the 
knowledge  of  customs,  of  genealogies,  of  languages, 
and  even  all  historical  knowledge  of  facts,  whether 
civil  or  natural;  these  are  useful  for  us  in  'avoiding 
dangers  and  in  taking  care  of  the  bodies  and  of  the 
men  whom  we  have  around  us,  but  they  do  not 
enlighten  the  mind.  The  knowledge  of  routes  is 
useful  to  a  traveller  while  he  is  on  his  journey,  but 
whatever  has  a  greater  relation  to  the  duties  that  lie 
before  him  in  patria  is  more  important  for  him. 
Now  we  are  destined  to  live  some  day  a  spiritual 
life,  where  substances  separated  from  matter  will 
occupy  us  much  more  than  do  the  bodies. 

Here  are  a  few  examples  taken  from  the  arts,  which 
will  enable  us  to  distinguish  between  that  which 
enlightens  the  mind  and  that  which  only  leads  it 
along  as  a  blind  man  might  be  led.  If  a  workman 
knows  by  experience  or  by  hearsay  that  when  the 
diameter  is  seven  feet  the  circumference  of  the 
circle  is  a  little  less  than  twenty-two  feet,  or  if  a  gun- 
ner knows  by  hearsay,  or  because  he  has  frequently 
measured  it,  that  bodies  are  thrown  the  farthest  at 
an  angle  of  45  degrees,  the  knowledge  is  confused 
and  is  that  of  an  artisan;  it  does  very  well  for  earn- 
ing a  living  and  for  performing  services  to  others, 
but  the  knowledge  which  enlightens  the  mind  is  that 
which  is  distinct,  or  which  gives  the  causes  or  rea- 
sons involved,  as  when  Archimedes  gave  the  demon- 
stration for  the  first  rule  and  Galileo  for  the  second. 
In  a  word,  it  is  only  knowledge  of  the  reasons  in 
themselves  or  of  the  necessary  eternal  truths,  above 
all  of  those  which  are  the  most  comprehensive  and 
which  have  the  most  relation  to  the  sovereign  being, 
that  are  able  to  make  us  more  perfect.  This  knowl- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          17 1 

edge  alone  is  good  in  itself;  all  the  rest  is  mercenary, 
and  should  be  learned  only  when  necessary  and  to 
serve  the  needs  of  this  life,  and  so  that  this  life  may 
be  in  a  better  position  to  contribute  afterwards  to 
the  perfection  of  the  mind  when  one's  subsistence 
has  been  provided  for.  But  the  intemperance  of 
men,  and  what  is  called  the  care  de pane  lucrando, 
and  often  also  vanity,  lead  us  to  forget  the  lord  for 
the  valet  and  the  end  for  the  means.  This,  accord- 
ing to  the  poet  is  "to  lose  the  reasons  for  living 
while  trying  to  live."  Very  much  as  a  miser  pre- 
fers gold  to  his  health,  while  gold  is  only  for  pro- 
curing the  commodities  of  life.  Now,  since  that 
which  perfects  the  mind  (leaving  aside  the  light  of 
grace),  is  the  demonstrative  knowledge  of  the  great- 
est truths  through  their  causes  or  reasons,  it  must  be 
granted  that  metaphysics  or  natural  theology  which 
treats  of  immaterial  substances  and  particularly  of 
God  and  of  the  soul,  is  the  most  important  of  all. 
One  cannot  go  very  far  in  this  without  inquiring 
into  the  true  conception  of  substance,  which  I,  in 
my  preceding  letter  to  M.  Arnaud  explained  in 
such  a  manner  that  he  himself  who  is  so  exact  and 
who  was  at  first  repelled  by  it,  accepted  it. 

Finally,  these  meditations  furnish  surprising  con- 
sequences which  are,  nevertheless,  of  wonderful  use 
in  freeing  men  from  doubts  regarding  the  relation  of 
God  to  created  things,  his  fore-knowledge  and  fore- 
ordination  and  the  union  of  the  soul  with  the  body, 
the  origin  of  evil  and  other  things  of  this  nature.  I 
say  nothing  here  of  the  great  applications  that  these 
principles  have  in  the  humanities,  but  at  least  I  am 
able  to  say  that  nothing  lifts  our  minds  more  to  the 
knowledge  and  to  the  love  of  God,  however  much 


172  CORRESPONDENCE. 

nature  may  help  us  in  this.  I  confess  that  all  these 
speculations  are  of  no  service  without  grace  and 
that  God  gives  grace  to  people  who  have  never 
dreamed  of  these  meditations,  but  God  wishes  also 
that  we  should  not  omit  anything  on  our  part  and 
that  each  one  of  us  according  to  his  vocation  and 
according  to  the  time,  should  make  use  of  the  per- 
fections which  God  has  given  to  human  nature. 
And  since  he  has  created  us  only  that  we  may  know 
and  love  him,  we  cannot  work  enough  toward  this 
nor  can  we  make  a  better  use  of  our  time  and  of  our 
energy  except  when  we  are  occupied  elsewhere  for 
the  public  and  for  the  welfare  of  others. 

XVI 

Arnauld  to  Leibniz. 

March  4th,  1687. 

It  has  been  a  long  time,  M.,  since  I  received  your 
letter,  but  I  have  been  so  busy  since  then  that  I  have 
not  been  able  to  reply  to  it  earlier. 

I  do  not  understand  very  well  what  you  mean  by 
this  "distincter  expression  which  our  soul  bears  of 
that  which  is  now  happening  to  its  body,"  and 
how  it  comes  about  that  when  someone  pricks  my 
finger  my  soul  knows  of  this  pricking  before  it  feels 
the  pain  of  it.  This  very  "distincter  expression," 
etc.,  ought  to  let  it  know  therefore  an  infinity  of 
other  things  which  happen  in  my  body  which,  never- 
theless, it  does  not  know,  for  instance  all  that  goes 
on  in  the  process  of  digestion  and  of  nutrition. 

As  for  your  saying  that  although  my  arm  raises 
itself  when  I  wish  to  raise  it,  it  is  not  because  my 
soul  causes  this  movement  in  my  arm  but  it  is 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  173 

because  "when  I  wish  to  raise  it  it  is  exactly  at  the 
very  moment  when  everything  is  ready  in  the  body 
for  this  very  effect,  in  such  a  way  that  the  body 
moves  itself  by  virtue  of  its  own  laws,  although  it 
happens  through  the  wonderful  but  unfailing  agree- 
ment of  things  among  themselves  that  these  laws 
conspire  together  at  the  very  same  moment  that  the 
will  makes  its  resolution.  For  God  had  regard 
to  this  in  advance  when  he  resolved  upon  this 
sequence  of  all  the  things  in  the  universe."  It 
seems  to  me  that  this  is  to  say  the  same  thing  in 
other  terms  that  those  say  who  maintain  that  my 
will  is  the  occasional  cause  for  the  movement  of  my 
arm  and  that  God  is  its  real  cause;  for  they  do  not 
claim  that  God  does  this  at  the  moment  by  a  new 
act  of  will  each  time  that  I  wish  to  raise  my  arm, 
but  by  a  single  act  of  the  eternal  will  by  which  he 
has  chosen  to  do  everything  which  he  has  foreseen 
that  it  will  be  necessary  to  do,  in  order  that  the  uni- 
verse might  be  such  as  he  has  decided  it  ought  to  be. 
Does  not  what  you  say  come  to  this  very  thing, 
namely  that  the  cause  of  the  movement  of  my  arm 
when  I  wish  to  lift  it  is  "the  wonderful  but  unfailing 
agreement  of  things  among  themselves  which  results 
because  God  had  them  in  mind  in  advance  when  he 
resolved  upon  this  sequence  of  all  the  things  in  the 
universe"?  For  this  forethought  of  God  has  not 
been  able  to  bring  about  any  event  without  a  real 
cause.  We  must,  therefore,  find  the  real  cause  of 
this  movement  of  my  arm.  You  do  not  wish  it  to 
be  my  will.  I  do  not  think,  either,  that  you  believe 
a  body  can  move  itself  or  any  other  body  as  a  real 
or  efficient  cause.  There  remains  therefore  only  this 
"forethought  of  God,"  which  can  be  the  real  and 


174  CORRESPONDENCE. 

efficient  cause  of  the  movement  of  my  arm.  Now 
you,  yourself,  called  this  forethought  of  God  his 
resolve;  and  resolve  and  will  are  the  same  thing. 
Therefore,  according  to  you,  every  time  that  I  wish 
to  raise  my  arm,  it  is  the  will  of  God  which  is  the 
real  and  efficient  cause  of  this  movement. 

In  regard  to  the  second  difficulty,  I  now  under- 
stand your  position  to  be  very  different  from  what  I 
thought,  for  I  supposed  that  you  would  reason  thus: 
the  body  should  be  the  true  substance;  now  there 
can  be  no  true  substances  which  have  no  true  unity 
nor  can  there  be  any  true  unity  which  has  not  a  sub- 
stantial form;  therefore  the  essence  of  a  body  can- 
not be  its  extension,  but  every  body  besides  its 
extension  should  have  a  substantial  form.  To  this 
I  have  replied  that  a  divisible  substantial  form,  such 
as  almost  all  those  who  hold  to  substantial  forms 
understand  them,  could  not  give  to  a  body  any  unity 
that  it  did  not  have  without  this  substantial  form. 

You  agree,  but  you  claim  that  every  substantial 
form  is  indivisible,  indestructible  and  ingenerable, 
being  produced  only  by  a  real  creation;  whence  it 
follows: 

ist.  That  every  body  which  can  be  divided  so  that 
each  part  will  remain  of  the  same  nature  as  the 
whole,  such  as  metals,  stones,  wood,  air,  water  and 
the  other  fluid  bodies,  have  no  substantial  form. 

2nd.  That  the  plants  have  none,  either,  since  a 
part  of  a  tree,  whether  placed  in  the  ground  or 
grafted  to  another  tree,  remains  a  tree  of  the  same 
sort  that  it  was  before. 

3rd.  That  only  animals  have  substantial  forms, 
and  that  therefore  in  your  opinion  only  animals  are 
true  substances. 


LEIBNIZ.        ARNAULD.        HESSEN-RHEINFELS.  175 

4th.  And  since,  as  you  say,  you  are  not  very  sure 
whether  brutes  have  souls  or  substantial  forms,  it 
follows  that  with  the  exception  of  man  there  is 
nothing  substantial  in  the  visible  world,  because  you 
claim  that  substantial  unity  requires  a  complete 
being,  indivisible,  and  through  natural  means  inde- 
structible. This  can  be  found  only  in  a  soul  or  a 
substantial  form  like  that  which  I  call  the  Me. 

All  of  this  means  that  every  body  whose  parts  are 
only  mechanically  united  is  not  a  substance  but 
only  a  machine  or  an  aggregate  of  several  sub- 
stances. 

I  will  begin  with  this  last.  And  I  will  say 
frankly  that  it  is  only  a  dispute  regarding  a  word. 
For  St.  Augustine  did  not  hesitate  to  recognize  that 
bodies  have  no  real  unity;  because  a  unit  should  be 
indivisible  and  no  body  is  indivisible.  There  is, 
therefore,  no  true  unity  excepting  in  Spirit,  any 
more  than  there  is  a  true  Me  outside  of  them. 
Now,  what  is  your  conclusion  from  that?  "That 
there  is  nothing  substantial  in  those  bodies  which 
have  no  soul  or  substantial  form."  In  order  that 
this  conclusion  may  be  valid  we  must  first  of  all 
define  substance  and  substantial  in  these  terms,  "I 
call  substance  and  substantial  that  which  has  a  true 
unity."  But  since  this  definition  has  not  yet  been 
received  there  is  no  philosopher  who  has  not 
as  much  right  to  say,  "I  call  substance  that 
which  is  not  modality  or  manner  of  being,"  and 
he  could  therefore  maintain  that  it  is  untrue  to 
say  that  there  is  nothing  substantial  in  a  block  of 
marble,  "because  this  block  of  marble  is  by  no 
means  a  manner  of  being  of  another  substance,  and 
all  that  can  be  said  of  it  is  that  it  is  not  a  single 


176  CORRESPONDENCE. 

substance  but  several  substances  joined  together 
mechanically."  This  philosopher  would  say  "this 
is  what  seems  to  me  paradoxical:  that  there  should 
be  nothing  substantial  in  that  which  seems  to  be 
made  up  of  several  substances."  He  could  add 
that  he  understood  still  less  what  you  meant  by  the 
words  "bodies  would  be  without  doubt  something 
imaginary  and  only  of  appearance  if  they  were  com- 
posed only  of  matter  and  its  modifications."  For 
you  postulate  only  matter  and  its  modifications  in 
everything  that  has  no  soul  or  no  substantial,  inde- 
structible, indivisible  and  ingenerable  form  and  it 
is  only  in  the  case  of  animals  that  you  admit  this 
class  of  forms.  You  will  therefore  be  obliged  to  say 
that  all  the  rest  of  nature  is  something  imaginary 
and  merely  an  appearance,  and  for  a  still  stronger 
reason  you  would  have  to  say  the  same  thing  of  all 
the  works  of  men. 

I  cannot  agree  to  these  latter  propositions,  but  I 
see  no  objection  to  thinking  that  in  every  corporeal 
nature  there  is  only  a  machine  and  an  aggregate  of 
substances,  because  of  no  one  of  its  parts  could  one 
say  strictly  that  it  is  a  single  substance.  This 
serves  merely  to  make  evident  what  is  worth  while 
noticing,  as  St.  Augustine  has  done,  that  the 
substance  which  thinks,  or  a  spiritual  substance, 
is  through  this  fact  much  more  excellent  than 
extended  or  corporeal  substance.  The  spiritual 
substance  alone  has  a  true  unity  and  a  true  ego, 
while  the  corporeal  substance  does  not  have  them. 
It  follows  from  this,  that  this  fact,  that  the  body  has 
no  true  unity  when  its  essence  is  extension,  cannot 
be  put  forward  to  prove  that  extension  is  not  of  the 
essence  of  the  body;  for,  perhaps,  the  essence  of 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          177 

the  body  has  no  true  unity,  as  you  grant  in  the  case 
of  all  those  which  are  not  united  to  a  soul  or  to  a 
substantial  form. 

I  do  not  know,  M.,  what  inclined  you  to  believe 
that  brutes  have  these  souls  or  substantial  forms, 
which,  according  to  you,  must  be  indivisible,  inde- 
structible and  ingenerable.  It  is  not  because  you 
consider  it  necessary  to  explain  their  actions,  for 
you  say  expressly  "that  all  the  phenomena  can  be 
explained  mechanically  or  by  the  corpuscular 
philosophy  in  accordance  with  certain  postulated 
mechanical  principles,  without  going  into  the  ques- 
tion whether  there  are  souls  or  not."  It  is  also  not 
because  the  bodies  of  brutes  need  to  have  a  true 
unity  and  because  they  are  not  mere  machines  or 
aggregations  of  substances;  if  plants  are  merely  the 
latter  what  necessity  is  there  that  brutes  should  be 
anything  else?  Further,  it  is  not  clear  how  this 
opinion  can  be  easily  maintained,  if  we  consider 
these  souls  as  indivisible  and  indestructible.  What 
would  be  said  of  a  worm,  of  which,  when  cut  in  two, 
both  parts  move  off  as  before?  If  a  house  where  a 
hundred  thousand  silk-worms  were  being  kept  should 
catch  fire  and  burn  up,  what  would  become  of 
those  one  hundred  thousand  indestructible  souls? 
Would  they  exist  apart  from  all  matter  like  our 
souls?  In  the  same  way,  what  became  of  the  souls 
of  those  millions  of  frogs  which  Moses  caused  to 
die  when  he  stopped  the  plague?  And  of  that 
innumerable  number  of  quails  which  the  Israelites 
killed  in  the  desert  or  of  all  the  animals  which 
perished  in  the  flood?  There  are  also  other  embar- 
rassing questions  in  regard  to  the  condition  of  these 
souls  in  each  brute  at  the  moment  that  they  are  con- 


178  CORRESPONDENCE 

ceived.  Is  it  that  they  are  in  seminibus  ?  Are  they 
there  indivisible  and  indestructible?  Quid  ergo  fit, 
cum  irrita  cadunt  sine  ullis  conceptions  semina  ?  Quid 
cum  bruta  mascula  ad  foeminas  non  accedunt  toto  vitae 
suae  tempore  ?  It  will  suffice  to  have  indicated  these 
difficulties. 

There  still  remains  the  discussion  of  the  unity 
which  a  reasoning  soul  has.  It  is  agreed  that  it  has 
a  true  and  a  perfect  unity,  a  true  Me,  and  that  it 
communicates  in  some  sort  this  unity  and  this 
Me  to  that  composite  whole  of  the  soul  and  body 
which  is  called  the  man;  for,  although  this  whole  is 
not  indestructible  because  it  perishes  when  the  soul 
is  separated  from  the  body,  it  is  indivisible  in  this 
sense,  that  half  a  man  cannot  be  conceived  of.  In 
considering  the  body  apart,  however,  in  the  same 
way  that  our  soul  does  not  communicate  to  it  its 
indestructibility,  we  cannot  see,  properly  speaking, 
that  it  communicates  either  its  true  unity  or  its 
indivisibility.  Even  though  it  be  united  to  our 
soul,  nevertheless,  its  parts  are  truly  united  among 
themselves  only  mechanically,  and  thus  there  is  not 
a  single  bodily  substance,  but  an  aggregation  of 
many  corporeal  substances.  Not  less  true  is  it  that 
it  is  quite  as  divisible  as  all  the  other  bodies  in 
nature.  The  divisibility,  however,  is  inconsistent 
with  unity,  therefore  it  has  no  true  unity.  But  you 
say,  it  acquires  the  unity  through  the  soul,  that  is  to 
say,  because  it  belongs  to  a  soul  which  is  a  true 
unit;  this,  however,  is  not  an  intrinsic  unity  in  the 
body,  but  is  like  that  of  different  provinces  which 
are  governed  by  a  single  king  and  thus  constitute 
one  kingdom. 

Although,  however,  it  is  true  that  there  is  no  real 


LEIBNIZ.       ARNAULD.       HESSEN-RHKINFELS.          179 

unity  except  in  intelligent  natures,  each  of  which 
can  say  the  word  Me^  there  are,  nevertheless,  differ- 
ent degrees  in  this  inexact  unity  which  belongs  to 
bodies;  for  although  there  are  no  bodies  which  are 
not  made  up  of  several  substances  there  is,  never- 
theless, reason  for  attributing  more  unity  to  those 
whose  parts  work  together  for  a  similar  purpose  like 
a  house  or  a  watch  than  to  those  whose  parts  are  only 
in  contact  one  with  another  like  a  pile  of  stones  or 
a  bag  of  coins  and  only  these  latter  can  properly  be 
called  an  accidental  aggregation.  Almost  all  natural 
bodies,  which  we  call  one,  like  a  piece  of  gold,  a 
star,  a  planet,  are  of  the  first  kind;  but  there  are 
none  which  appear  to  be  more  so  than  the  organized 
bodies,  that  is,  the  animals  and  plants;  though  there 
is  no  reason  to  assign  souls  to  them  on  this  account 
(and  I  think  also  that  you  assigned  none  to  plants). 
For  why  should  not  a  horse  or  an  orange  be  consid- 
ered each  one  as  a  complete  and  whole  work  quite 
as  well  as  a  church  or  a  watch  ?  What  is  essential  in 
order  that  a  thing  may  be  called  one  (that  is,  this 
oneness  which  applies  to  bodies,  but  which  is  very 
different  from  that  that  applies  to  spiritual  natures) 
when  the  parts  are  united  among  themselves  only 
mechanically  as  are  the  parts  of  the  machine?  Is 
it  not  the  greatest  perfection  that  they  can  have, 
that  they  are  machines  so  wonderful  that  only  an 
all-powerful  God  could  have  constructed  them? 
Our  body,  considered  by  itself,  is  therefore  one  in 
this  sense.  The  relationship,  which  an  intelligent 
nature,  united  to  it  and  governing  it,  has  with  it, 
may,  perhaps,  add  some  unity,  but  it  is  not  that  kind 
of  unity  which  pertains  to  spiritual  natures. 

I  confess,  M.,  that  my  ideas  on  the  laws  of  motion 


l8o  CORRESPONDENCE. 

are  not  clear  and  distinct  enough  to  enable  me  to 
pass  judgment  upon  the  difficulty  which  you  have 
brought  up  against  the  Cartesians.  The  one  who 
replied  to  you  is  the  Abbe  Catelan  who  has  a  good 
mind  and  is  a  good  geometer;  since  I  left  Paris  I 
have  not  had  much  intercourse  with  the  philoso- 
phers of  that  country.  Inasmuch,  however,  as  you 
have  decided  to  reply  to  this  Abbe,  and  as  he  will 
perhaps  wish  to  defend  his  position,  it  is  to  be 
hoped  that  these  discussions  will  so  clear  up  the 
difficulty  that  it  will  be  possible  to  know  which  side 
to  take. 

I  thank  you  very  much  for  the  desire  you  show  to 
know  how  I  am.  I  am  thankful  to  say  that  I  am 
very  well  for  my  age,  only  I  had  a  very  bad  cold  at 
the  beginning  of  the  winter.  I  am  very  glad  that 
you  are  thinking  of  completing  your  arithmetical 
machine.  It  would  be  a  pity  if  so  fine  an  invention 
were  lost.  I  desire  greatly,  however,  that  the  inten- 
tion in  regard  to  which  you  wrote  a  word  to  the 
Prince,  who  has  so  much  affection  for  you,  may  not 
remain  without  its  effects,  for  there  is  nothing 
towards  which  a  wise  man  should  work  with  more 
care  and  with  less  of  delay  than  towards  what  has 
to  do  with  his  salvation.  I  am,  Monsieur, 
Your  very  humble  and  obedient  servant. 

A.  ARNAULD. 
XVII 
Leibniz  to  Arnauld. 

Gottingen,  April  30,  1687. 
Monsieur: 

Since  I  regard  your  letters  as  personal  benefactions 
to  me  and  as  sincere  marks  of  your  liberality,  I 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          l8l 

have  no  right  to  ask  for  them  and  consequently 
your  reply  is  never  too  late.  However  agreeable 
and  useful  they  may  be  to  me,  I  take  into  con- 
sideration what  you  owe  to  the  public  weal  and 
thus  suppress  my  desires.  Your  criticisms  are 
always  instructive  and  I  will  take  the  liberty  to  go 
through  them  in  order. 

I  do  not  think  that  there  is  any  difficulty  in  my 
saying  that  "the  soul  expresses  more  distinctly, 
other  things  being  equal,  that  which  pertains  to  its 
own  body";  since  it  expresses  the  whole  universe 
in  a  certain  sense  according  to  the  special  relation 
of  other  bodies  to  itself,  it  is  not  able  to  express  all 
things  equally,  otherwise  there  would  be  no  distinc- 
tion between  souls,  but  it  does  not  follow  from  this 
that  the  soul  should  perceive  perfectly  whatever 
goes  on  in  the  parts  of  its  body,  since  there  are 
degrees  of  relationship  between  these  parts  them- 
selves and  these  parts  are  no  more  equally  expressed 
than  are  external  things.  The  greater  distance  of 
the  latter  is  made  up  for  by  the  smallness  or  by 
some  other  hindrance  in  the  internal  parts.  Thales 
saw  the  stars  though  he  did  not  see  the  ditch  which 
was  at  his  feet. 

The  nerves  and  membranes  are  for  us  the  parts 
which  are  more  sensitive  than  the  others  and  it  is,  per- 
haps, only  through  them  that  we  perceive  what  seems 
to  happen  to  the  others,  because  the  movements  of 
the  nerves,  or  of  the  liquids  in  them,  imitate  the 
impressions  better  and  confuse  them  less,  and  the 
most  distinct  expressions  of  the  soul  correspond  to 
the  most  distinct  impressions  of  the  body.  Meta- 
physically speaking,  it  is  not  the  nerves  which  act 
upon  the  soul,  but  the  one  represents  the  state  of  the 


1 82  CORRESPONDENCE. 

other  through  the  spontaneous  relation;  it  must  also 
be  remembered  that  too  many  things  take  place 
within  our  bodies  to  be  all  separately  perceived;  we 
feel  only  a  certain  result,  to  which  we  are  accus- 
tomed, and  we  are  not  able  to  distinguish  the  ele- 
ments that  are  involved,  because  of  their  multitude. 
Just  as  when  we  hear  from  afar  the  sound  of  the  sea, 
we  do  not  distinguish  what  each  wave  does,  although 
each  wave  has  its  effect  upon  our  ears.  When 
a  striking  change  happens  in  our  body,  we  notice  it 
at  once  and  more  clearly  than  the  changes  outside, 
which  are  not  accompanied  by  any  special  change 
in  our  organs. 

I  do  not  say  that  the  soul  knows  the  pricking 
before  it  has  the  sense  of  pain,  except  as  it  knows 
or  expresses  confusedly  all  things  in  accordance 
with  the  principles  already  established.  This  expres- 
sion, however,  although  obscure  and  confused, 
which  the  soul  has  in  advance  of  the  future,  is  the 
real  cause  of  that  which  happens  to  it  and  of  the 
clearer  conception  which  it  will  have  later  when 
the  obscurity  shall  have  worked  out.  The  future 
state  is  only  a  consequence  of  the  preceding. 

I  said  that  God  created  the  universe  in  such  a  way 
that  the  soul  and  the  body,  each  acting  according  to 
its  laws,  agree  in  their  phenomena.  You  think,  M., 
that  this  coincides  with  the  hypothesis  of  occasional 
causes.  Were  this  so  I  should  not  be  sorry,  and  I 
am  always  glad  to  find  those  who  hold  my  positions. 
I  see,  however,  the  reason  for  your  thinking  this. 
You  are  of  the  opinion  that  I  would  not  say  a  body  can 
move  itself,  and,  the  soul  not  being  the  real  cause 
either  of  the  motion  of  the  arm  or  of  the  body,  there- 
fore the  cause  must  be  God.  My  opinion,  how- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          183 

ever,  is  different.  I  hold  that  whatever  reality  there 
is  in  the  state  which  is  called  motion,  may  issue 
quite  as  well  from  the  bodily  substance  as  the 
thought  and  will  proceed  from  the  spirit.  Every- 
thing happens  to  each  substance  in  consequence  of 
the  first  state  which  God  gave  to  it  in  creating  it, 
and  putting  aside  extraordinary  interventions  the 
ordinary  agreement  consists  only  in  the  conserva- 
tion of  the  substance  itself  conformably  to  its  pre- 
ceding state  and  to  the  changes  which  it  carries  in 
itself.  Nevertheless,  we  have  the  right  to  say  that 
one  body  pushes  another;  that  is  to  say,  that  one 
body  never  begins  to  have  a  certain  tendency  except- 
ing when  another  which  touches  it  loses  proportion- 
ately, according  to  the  constant  laws  which  we  observe 
in  phenomena;  and  since  movements  are  rather  real 
phenomena  than  beings,  a  movement  as  a  phenom- 
enon is  in  my  mind  the  immediate  consequence  or 
effect  of  another  phenomenon,  and  the  same  is  true 
in  the  minds  of  others  The  condition  of  one  sub- 
stance, however,  is  not  the  immediate  consequence 
of  the  condition  of  another  particular  substance. 

I  dare  not  maintain  that  plants  have  no  souls,  nor 
life,  nor  any  substantial  form;  since,  although  one 
part  of  a  tree  planted  or  grafted  can  produce  a  tree 
of  the  same  kind,  it  is  possible  that  there  is  in  it  a 
seminal  part  which  already  contains  a  new  plant,  as 
it  is  likely  there  are  living  animalcula  although 
very  small  in  the  seed  of  animals  which  can  be 
transformed  into  a  similar  animal;  I  do  not  there- 
fore dare  to  maintain  that  animals  alone  are  living 
and  endowed  with  substantial  forms.  Perhaps  there 
is  an  infinity  of  degrees  in  the  forms  of  corporeal 
substances. 


184  CORRESPONDENCE. 

You  say,  M.,  that  "those  who  hold  to  the  hypoth- 
esis of  occasional  causes,  saying  that  my  will  is 
the  occasional  cause,  while  God  is  the  real  cause  of 
the  movement  of  my  arm,  do  not  claim  that  God 
does  this  at  the  moment  by  a  new  volition,  which 
he  has  each  time  I  wish  to  lift  my  arm,  but  through 
that  single  act  of  eternal  will,  by  which  he  resolved 
to  do  everything  which  he  foresaw  would  be  neces- 
sary for  him  to  do."  To  this  I  reply  that  we  can 
say  with  the  same  reasoning,  that  miracles  also  are 
not  the  result  of  a  new  act  of  will  on  God's  part, 
being  conformable  to  a  general  plan;  and  I  have 
already  stated,  in  what  precedes,  that  every  act  of 
will  on  God's  part  involves  all  the  others,  but  with  a 
certain  order  of  priority;  if  I  properly  understand 
the  position  of  the  authors  of  occasional  causes,  they 
introduce  a  miracle  which  is  not  less  miraculous 
for  being  continual,  for  it  seems  to  me  that  infre- 
quency  does  not  constitute  the  conception  of  mir- 
acle. It  will  be  said  that  God  acts  in  that,  only 
according  to  a  general  rule  and  consequently  with- 
out miracle,  but  I  do  not  grant  this  consequence  and 
I  think  that  God  could  make  general  rules  with 
regard  to  the  miracles  themselves.  For  instance, 
if  God  resolved  to  give  his  grace  immediately,  or  to 
perform  some  other  action  of  this  nature  every  time 
that  a  certain  condition  came  about,  this  action 
would,  nevertheless,  be  a  miracle  although  quite  in 
the  ordinary.  I  confess  that  the  authors  of  occas- 
ional causes  can  give  another  definition  of  the  term, 
but  it  seems  that  according  to  usage  a  miracle 
differs  internally  and  substantially  from  that  which 
results  from  ordinary  activity,  and  its  distinctiveness 
does  not  depend  upon  its  unusualness;  properly 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         185 

speaking,  God  performs  a  miracle  when  he  does  any- 
thing which  surpasses  the  powers  which  he  has  given 
to  created  things  and  which  he  maintains  in  them;  for 
example,  if  God  should  make  a  body,  which  was 
put  in  circular  motion  by  means  of  a  sling,  to  go  on 
freely  in  a  circular  line  even  when  it  was  released 
from  the  attachment,  this,  when  it  was  neither 
pushed  nor  retained  by  anything,  would  be  a  mir- 
acle, for,  according  to  the  laws  of  Nature  the  body 
should  travel  along  the  line  of  the  tangent:  if,  more- 
over, God  should  decide  that  such  should  always  be 
the  case,  he  would  perform  a  natural  miracle,  for 
this  movement  could  not  be  explained  by  anything 
more  simple.  In  the  same  way,  we  should  have  to 
say  in  accordance  with  the  current  conception,  that 
if  the  continuation  of  the  motion  were  beyond  the 
power  of  bodies,  the  continuation  of  the  motion 
would  be  a  true  miracle;  while  my  position  is  that 
the  corporeal  substance  has  the  power  to  continue 
its  changes  according  to  the  laws  which  God  has 
put  into  its  nature  and  which  he  maintains  there. 

To  make  myself  better  understood  I  will  add  that 
the  activities  of  the  mind  change  nothing  at  all  in 
the  nature  of  the  body,  nor  the  body  in  that  of 
the  mind;  and  I  will  also  add  that  neither  does  God 
change  anything  on  the  occasion  of  their  action 
except  when  he  performs  a  miracle.  In  my  opin- 
ion, things  are  so  concerted  together  that  the  mind 
never  desires  anything  efficaciously  excepting  when 
the  body  is  ready  to  accomplish  it  in  virtue  of  its  own 
laws  and  forces;  while,  according  to  the  authors 
of  occasional  causes,  God  changes  the  laws  of  the 
body  on  the  occasion  of  the  action  of  the  soul  and,  vice 
versa.  That  is  the  essential  difference  between  our 


l86  CORRESPONDENCE. 

positions.  Therefore,  we  should  not  ask  how  the  soul 
can  give  any  motion  or  new  determination  to  the 
animal  spirits,  since  it  never  does  anything  of  the 
kind,  for  there  is  no  interaction  between  spirit  and 
body,  and  there  is  nothing  which  can  determine 
what  degree  of  velocity  a  mind  will  give  to  a  body, 
nor  what  degree  of  velocity  God  may  be  minded  to 
give  to  the  body  on  the  occasion  of  the  mind's  action 
according  to  a  certain  law.  The  same  difficulty  is 
found  with  regard  to  the  hypothesis  of  occasional 
causes  which  there  is  in  the  hypothesis  of  a  real 
influence  of  the  soul  upon  the  body  and  vice  versa; 
because  we  can  see  no  relation  or  basis  for  such  a 
rule.  If  one  were  to  say,  as  M.  Descartes  seems  to, 
that  the  soul,  or  God  on  the  occasion  of  its  acting, 
changes  merely  the  direction  or  determination  of  the 
motion  and  not  the  force  which  is  in  bodies,  (since 
it  does  not  seem  probable  to  him  that  God  would 
interrupt  at  each  moment  on  the  occasion  of  the 
willing  of  spirits,  this  general  law  of  nature, 
namely,  that  the  same  force  should  perdure),  I 
would  reply  that  it  will  be  quite  difficult  to  explain 
what  connection  there  can  be  between  the  thoughts 
of  the  soul  and  the  sides  or  the  angles  of  direc- 
tion of  bodies,  and  furthermore  that  there  is  in 
nature  another  general  law  which  M.  Descartes  has 
not  perceived  but  which  is,  nevertheless,  important 
— namely,  that  the  sum  total  of  the  determinations 
or  directions  must  always  perdure.  For  I  find  that 
if  any  straight  line  be  drawn,  for  example,  from 
east  to  west,  through  a  given  point,  and  if  all  the  direc- 
tions of  all  the  bodies  in  the  world  in  so  far  as  they 
advance  toward  or  move  away  in  lines  parallel  to 
this  line  be  calculated,  the  difference  between  the 


LEIBNIZ.       ARNAULD.       HESSKN-RHEINFELS.          187 

sums  of  the  quantities  of  all  the  easterly  direc- 
tions and  of  all  the  westerly  directions  will  ever  be 
found  the  same,  whether  certain  particular  bodies 
which  might  alone  be  supposed  to  have  relations 
among  themselves,  be  regarded  or  whether  the 
whole  universe  be  regarded.  In  this  latter  case 
the  difference  is  always  zero.  Everything  is  per- 
fectly balanced  and  the  easterly  and  westerly  direc- 
tions in  the  universe  are  exactly  equal.  If  God 
wished  to  do  anything  against  this  principle  it 
would  be  a  miracle. 

It  is  therefore  much  more  reasonable  and  more 
worthy  of  God  to  suppose  that  he  has  created  the 
machinery  of  the  world  in  such  a  fashion  from  the 
very  start,  that  without  doing  violence  at  every 
moment  to  the  two  great  laws  of  nature,  that  of 
force  and  that  of  direction,  but  rather  by  following 
them  exactly,  (except  in  the  case  of  miracles,)  it  so 
comes  about  that  the  internal  springs  of  bodies  are 
ready  to  act  of  themselves,  as  they  should,  at  the 
very  moment  when  the  soul  has  a  conforming 
desire  or  thought.  The  soul,  in  turn,  has  had  this 
desire  or  thought  only  conformably  to  preceding 
states  of  the  body  and  thus  the  union  of  the  soul 
with  the  machinery  of  the  body  and  with  the  parts 
which  compose  it,  and  the  action  of  the  one  upon 
the  other  consists  only  in  this  concomitance,  which 
betokens  the  wonderful  wisdom  of  the  Creator  much 
more  than  any  other  hypothesis.  It  cannot  be 
denied  that  this  at  least  is  possible,  and  that  God  is 
a  sufficiently  great  workman  to  be  able  to  carry  it 
out;  therefore,  it  can  easily  be  decided  that  this 
hypothesis  is  the  most  probable,  being  the  simplest 
and  most  intelligible  and  at  once  avoiding  all  diffi- 


1 88  CORRESPONDENCE. 

culties;  for  example,  the  difficulties  involved  in 
criminal  actions,  where  it  seems  much  more  reason- 
able to  let  God  intervene  only  through  the  conserva- 
tion of  the  created  forces. 

To  employ  a  comparison,  I  will  say  in  regard  to 
this  concomitance,  which  I  hold  to  be  true,  that  it 
is  like  several  bands  of  musicians  or  choirs  separ- 
ately taking  up  their  parts  and  placed  in  such  a  way 
that  they  neither  see  nor  hear  one  another,  though 
they  nevertheless,  agree  perfectly  in  following  their 
notes,  each  one  his  own,  in  such  a  way  that  he  who 
hears  the  whole  finds  in  it  a  wonderful  harmony 
much  more  surprising  than  if  there  were  a  connec- 
tion between  the  performers.  It  is  quite  possible 
also  that  a  person  who  is  close  by  one  of  two  such 
choirs  could  judge  from  the  one  what  the  other 
was  doing,  and  would  form  such  a  habit  (particularly 
if  we  supposed  that  he  was  able  to  hear  his  own  choir 
without  seeing  it  and  to  see  the  other  without  hear- 
ing it),  that  his  imagination  would  come  to  his  aid 
and  he  would  no  longer  think  of  the  choir  where  he 
was,  but  of  the  other,  and  he  would  take  his  own  for 
an  echo  of  the  other,  attributing  to  his  own  only 
certain  interludes,  in  which  certain  rules  of  sym- 
phony by  which  he  understood  the  other  did  not 
appear,  or  else  attributing  to  his  own  certain  move- 
ments which  he  caused  to  be  made  from  his  side, 
according  to  certain  plans  that  he  thought  were 
imitated  by  the  other  because  of  the  inter-relation- 
ship which  he  found  in  the  kind  of  melody,  not 
knowing  at  all  that  those  who  were  in  the  other 
choir  were  doing  also  something  which  corresponded 
according  to  their  own  plans. 

Nevertheless,    I  do  not  at  all  disapprove  of  the 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          189 

statement  that  minds  are  in  some  sort  the  occasional 
and  even  real  causes  of  certain  movements  in  the 
body,  for,  with  regard  to  the  divine  resolves,  what- 
ever God  has  foreseen  and  pre-established  with 
regard  to  minds,  has  been  an  occasion  for  his  thus 
regulating  the  body  from  the  very  start,  so  that 
they  might  fit  in  together,  each  following  the  laws 
and  forces  that  he  has  given  them;  and  as  the  state 
of  one  is  an  unfailing  consequence  of  the  other,  al- 
though frequently  contingent  and  even  free,  we  can 
say  that  God  has  established  a  real  connection  in 
virtue  of  this  general  conception  of  substances,  which 
brings  it  about  that  they  express  one  another  per- 
fectly. This  connection,  however,  is  not  immediate, 
being  founded  only  upon  what  God  has  given  them 
in  creating  them. 

If  my  opinion,  that  substances  require  a  true  unity, 
is  founded  only  upon  a  definition  which  I  have 
made  up  contrary  to  the  common  usage,  this  would 
be  a  mere  question  of  words;  but  besides  the  fact 
that  most  philosophers  have  understood  this  term 
in  nearly  the  same  way,  namely,  that  "a  distinction 
should  be  made  between  unity  through  itself  and 
unity  through  accident,  between  substantial  form  and 
accidental  form,  between  an  imperfect  and  a  perfect 
compound,  between  natural  and  artificial,"  I  take 
still  higher  ground  and,  leaving  the  question  of 
terminology,  I  believe  that  where  there  are  only 
beings  by  aggregation,  there  are  not  even  real  beings, 
because  every  being  by  aggregation  pre-supposes 
beings  endowed  with  true  unity,  because  it  ob- 
tains its  reality  only  from  the  reality  of  the  ele- 
ments of  which  it  is  composed,  so  that  it  will  have 
no  reality  at  all  if  every  being  of  which  it  is  com- 


IpO  CORRESPONDENCE. 

posed  is  again  a  being  by  aggregation;  or  else  we 
must  seek  some  other  foundation  for  its  reality, 
seeing  that  by  this  method  it  can  never  be  reached, 
even  by  searching  forever.  I  grant,  M.,  that  in  all 
corporeal  nature  there  exist  only  machines  (some  of 
which  are  alive),  but  I  do  not  grant  that  there  exist 
only  aggregations  of  substances,  and  if  there  do  exist 
aggregations  of  substances  it  must  be  that  there  are 
also  real  substances  of  which  all  these  aggregations 
are  the  product;  we  therefore  come  necessarily 
to  the  mathematical  points  out  of  which  certain 
writers  have  constructed  extension,  or  to  the  atoms 
of  Epicurus  and  of  M.  Cordemoy — things  which 
you  reject  quite  as  much  as  I  do;  or  else  we  must 
acknowledge  that  no  reality  is  to  be  found  in  bodies. 
The  other  alternative  is  to  say  that  there  are  certain 
substances  which  have  a  real  unity.  I  have  already 
said  in  another  letter  that  the  composite  of  the  dia- 
monds of  the  Grand  Duke  and  of  the  Great  Mogul 
could  be  called  a  pair  of  diamonds,  but  this  would 
only  be  a  being  of  the  reason,  and  if  they  were 
brought  together  they  would  become  a  being  of 
the  imagination  or  perception,  that  is  to  say, 
a  phenomenon,  because  contact,  common  move- 
ment and  even  agreement  in  design,  do  not  effect 
a  substantial  unity.  It  is  true  that  sometimes  there 
is  more  and  sometimes  less  basis  for  supposing 
that  several  things  constitute  one,  according  as  the 
things  have  more  or  less  connection, but  this  is  only  a 
means  to  abbreviate  our  thinking  and  to  represent 
the  phenomenon. 

It  seems  also  that  what  constitutes  the  essence  of  a 
being  by  aggregation  consists  solely  in  the  mode 
of  the  being  of  its  component  elements.  For  exam- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          191 

pie,  what  constitutes  the  essence  of  an  army?  It  is 
simply  the  mode  of  being  of  the  men  who  compose 
it.  This  mode  of  being  presupposes,  accordingly  a 
substance  of  which  the  essence  is  not  a  mode  of  being 
of  a  substance.  Every  machine  therefore  presup- 
poses some  substance  in  the  parts  out  of  which  it  is 
made,  and  there  is  no  plurality  without  true  unities; 
in  short,  I  consider  as  an  axiom  this  identical  propo- 
sition, which  receives  two  meanings  only  through  a 
change  in  accent;  namely,  that  what  is  not  truly  a 
being  is  not  truly  a  being.  It  has  always  been 
thought  that  one  and  being  are  reciprocal  terms. 
Being  is  very  different  from  beings,  but  the  plural 
presupposes  the  singular;  and  there  where  there  is 
no  being,  are  there  still  less  several  beings.  What 
can  be  clearer?  I  thought,  therefore,  that  I  should 
be  permitted  to  distinguish  beings  by  aggrega- 
tion from  substances,  since  these  beings  have  their 
unity  only  in  our  minds,  and  our  minds  repose 
upon  the  relations  or  the  modes  of  real  substances. 
If  a  machine  is  a  substance,  a  circle  of  men  who  are 
holding  hands  would  be  one  also,  so  an  army,  and 
in  fact,  any  gathering  together  of  substances.  I  do 
not  say  that  there  is  nothing  substantial  or  nothing 
but  appearance  in  things  which  have  not  a  true  unity, 
for  I  acknowledge  that  they  have  as  much  of  reality 
or  substantiality  as  there  is  of  true  unity  in  that 
which  enters  into  their  composition. 

You  object,  M.,  that  it  might  be  of  the  essence 
of  bodies  to  have  no  true  unity.  But  it  will  be  then 
the  essence  of  bodies  to  be  phenomena  deprived 
of  all  reality  as  would  be  an  orderly  dream,  for 
phenomena,  like  the  rainbow  or  like  a  pile  of  stones, 
will  be  wholly  imaginary  if  they  are  not  com- 


I9«  CORRESPONDENCE. 

posed  of  beings  which  have  a  true  unity.  You 
say  that  you  do  not  see  why  I  admit  substantial 
forms  or  rather  corporeal  substances  endowed  with 
a  true  unity.  It  is  because  I  can  conceive  of  no 
reality  without  a  true  unity,  and  in  my  opinion  the 
concept  of  the  singular  substance  involves  conse- 
quences incompatible  with  its  being  a  mere  aggre- 
gation. I  can  conceive  of  properties  in  the  sub- 
stance which  cannot  be  explained  by  extension,  by 
form  and  by  motion,  quite  apart  from  the  fact  that 
there  is  no  exact  and  definite  form  in  bodies  because 
of  the  actual  subdivision  of  the  continuum  to  infin- 
ity, and  that  their  motion  in  so  far  as  it  is  only  a 
modification  of  extension  and  a  change  of  place, 
involves  something  imaginary  so  that  we  cannot 
determine  to  which  object,  among  those  that  change, 
it  belongs,  unless  we  have  recourse  to  the  force  that 
is  the  cause  of  the  motion  and  that  inheres  in  the 
corporeal  substance.  I  confess  that  there  is  no  need 
of  mentioning  these  substances  and  qualities  in 
explaining  particular  phenomena,  but  no  more  is 
there  need  of  inquiring  about  the  intervention  of 
God,  the  composition  of  the  continuum,  the  plenum, 
and  a  thousand  other  things.  The  particular  events 
of  nature  I  confess  can  be  explained  mechanically, 
but  only  after  having  recognized  or  presupposed  the 
principles  of  mechanics.  These  can  be  established 
a  priori  only  through  metaphysical  speculations. 
The  difficulties  involved  in  the  composition  of  the 
continuum  will  never  be  resolved  so  long  as  exten- 
sion is  considered  as  constituting  the  substance  of 
the  bodies,  and  we  shall  find  ourselves  entangled 
in  our  own  chimeras. 

I  think  furthermore  that  to  attempt  to  limit  true 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         193 

unity  or  substance  to  man  alone  is  as  shortsighted 
in  metaphysics  as  it  was  in  the  realm  of  physics 
to  desire  to  enclose  the  world  in  a  sphere.  And 
since  true  substances  are  so  many  expressions  of  the 
whole  universe  taken  in  a  certain  sense  and  so  many 
reduplications  of  the  divine  work,  it  is  in  conformity 
with  the  grandeur  and  the  beauty  of  the  works  of 
God,  (seeing  that  these  substances  do  not  clash  with 
one  another,)  to  create  in  this  universe  as  many  of 
them  as  is  possible  and  as  superior  reasons  permit. 
The  wholly  bare  supposition  of  extension  destroys 
this  wonderful  variety,  since  mass,  by  itself  (if  we 
were  able  to  conceive  of  it),  is  as  much  inferior  to 
a  substance  which  is  perceptive  and  which  rep- 
resents the  whole  universe  according  to  its  point 
of  view  and  according  to  the  impressions  or  rather 
relations  that  its  body  receives  mediately  or  im- 
mediately from  all  others,  as  a  dead  body  is  below 
an  animal  or  as  a  machine  is  inferior  to  a  man. 
It  is,  indeed,  through  the  idea  of  substance  that 
the  evidences  of  the  future  are  formed  in  advance 
and  that  the  traces  of  the  past  are  preserved 
forever  in  everything,  and  that  cause  and  effect 
are  exactly  equivalent  even  to  the  slightest  circum- 
stance, although  each  effect  depends  upon  an  infinity 
of  causes  and  every  cause  has  an  infinity  of  effects. 
It  would  not  be  possible  to  obtain  this  state  of 
things,  if  the  essence  of  the  body  consisted  only  in 
a  certain  form,  motion  or  modification  of  extension, 
which  was  predetermined.  Furthermore,  there  is 
nothing  of  the  kind  in  nature;  taken  strictly,  every 
thing  is  indefinite  with  regard  to  extension,  and 
whatever  we  attribute  to  bodies  are  only  phenom- 
ena and  abstractions:  this  enables  us  to  see  how 


194  CORRESPONDENCE. 

easy  it  is  to  fall  into  error  if  reflections  so  necessary 
for  recognizing  the  true  principles  and  for  having  a 
valid  idea  of  the  universe  are  not  made.  It  seems 
to  me  that  as  much  prejudice  is  displayed  in  refus- 
ing to  accept  so  reasonable  an  idea  as  this,  as  there 
would  be  in  not  recognizing  the  grandeur  of  the 
world,  the  subdivision  to  infinity  and  the  mechani- 
cal explanations  of  nature.  It  is  as  great  an  error 
to  conceive  of  extension  as  a  primitive  concept 
without  looking  into  the  real  concept  of  substance 
and  of  action,  as  it  was  formerly  to  be  contented 
with  considering  substantial  forms  as  a  whole  with- 
out entering  into  details  as  to  the  modifications  of 
extension. 

The  great  number  of  souls  (to  which,  however,  I 
do  not  necessarily  attribute  in  every  case  pain  and 
pleasure),  should  not  trouble  us  any  more  than  do 
the  great  number  of  the  atoms  put  forward  by  Gas- 
sendi,  which  are  quite  as  indestructible  as  the  soul. 
On  the  contrary  it  is  one  of  the  perfections  of 
nature  to  have  so  many  of  them,  since  a  soul  or 
indeed  a  living  substance  is  infinitely  more  perfect 
than  an  atom,  which  is  without  variety  or  subdivis- 
ion. Every  living  thing  contains  a  world  of  diver- 
sity in  a  real  unity.  Our  experience  is  in  favor  of 
this  great  number  of  living  things;  we  find  that  there 
is  a  prodigious  quantity  of  them  in  a  drop  of  water 
tinctured  with  powder  and  with  one  blow  millions 
of  them  can  be  killed  so  that  neither  the  frogs  of 
the  Egyptians  nor  the  quails  of  the  Israelites  of 
which  you  spoke,  M.,  at  all  approach  the  number. 
Now,  if  these  animals  have  souls,  the  same  must  be 
said  of  their  souls  which  can  probably  be  said  of  the 
animals  themselves;  namely,  that  they  have  been 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          195 

living  from  the  very  creation  of  the  world  and  that 
they  will  live  to  its  end,  and  that  birth  being  appar- 
ently only  a  change  consisting  in  growth,  so  death 
is  only  a  change  or  diminution  which  causes  this 
animal  to  re-enter  into  the  engulfing  of  a  world  of 
minute  creatures,  where  perceptions  are  very  lim- 
ited until  the  command  comes  calling  them  to  return 
to  the  theater  of  action.  The  ancients  made  the 
mistake  of  introducing  the  transmigration  of  souls, 
in  place  of  the  transformation  of  the  same  animal 
which  always  preserves  the  same  soul.  They  put 
metempsychoses  in  place  of  metaschematismi. 
Spirits,  however,  are  not  subjected  to  these  revolu- 
tions, or  rather  these  revolutions  of  bodies  must 
serve  the  divine  economy  for  the  sake  of  spirits. 
God  creates  them  when  it  is  time  and  he  detaches 
them  from  the  body,  at  least  from  the  material 
body  by  death;  since  they  must  always  preserve 
•their  moral  qualities  and  their  memory  in  order  to 
be  perpetual  citizens  of  that  universal  republic, 
absolutely  perfect,  whose  monarch  is  God.  This 
republic  can  never  lose  any  of  its  members  and  its 
laws  are  superior  to  those  of  the  body.  I  grant  that 
bodies  by  themselves  without  the  soul  have  only  a 
unity  of  aggregation,  but  the  reality  which  inheres 
in  them  comes  from  the  parts  which  compose  them 
and  which  retain  their  substantial  unity  through  the 
living  bodies  that  are  included  in  them  without  num- 
ber. 

Nevertheless,  although  it  is  possible  that  a  soul 
have  a  body  made  up  of  animated  parts  or  of  separ- 
ate souls,  the  soul  or  the  form  of  the  whole  is  not, 
therefore,  composed  of  souls  or  forms  of  parts.  In 
regard  to  an  insect  which  is  cut  in  two,  it  is  not 


196  CORRESPONDENCE. 

necessary  that  the  two  parts  shall  remain  animated, 
although  there  may  be  some  movement  in  them,  at 
least  the  soul  of  the  whole  insect  will  remain  only 
on  one  side  and  as  in  the  formation  and  in  the 
growth  of  the  insect  the  soul  has  already  been  in  a 
certain  part  alive  from  the  very  start,  it  will  remain 
also  after  the  destruction  of  the  insect,  still  alive  in 
.  a  certain  part,  which  will  always  be  as  small  as  is  nec- 
essary to  serve  as  an  asylum  from  the  action  of  him 
who  is  tearing  or  destroying  the  body  of  this  insect. 
We  need  not,  however,  imagine  with  the  Jews  that 
there  is  a  little  bone  of  irrefrangible  hardness  where 
the  soul  preserves  itself. 

I  agree  that  there  are  degrees  of  accidental  unity, 
that  a  regulated  society  has  more  unity  than  a  con- 
fused mob  and  that  an  organized  body  or  indeed  a 
machine  has  more  unity  than  a  society.  That  is, 
it  is  more  appropriate  to  conceive  of  them  as  a  sin- 
gle thing  because  there  is  more  relation  between 
the  component  elements.  All  these  unities,  how- 
ever, receive  their  name  only  through  thoughts  and 
through  appearances  like  colors  and  other  phenom- 
ena that  are,  nevertheless,  called  real.  The  fact  that 
a  pile  of  stones  or  a  block  of  marble  can  be  touched 
does  not  prove  its  substantial  reality  any  more  suc- 
cessfully than  the  visibility  of  a  rainbow  proves 
its  reality;  and  as  nothing  is  so  solid  that  it  has  not 
a  certain  degree  of  fluidity,  perhaps  the  block  of 
marble  itself  is  only  a  mass  of  an  infinite  number 
of  living  bodies  like  a  lake  full  of  fish,  although 
such  animals  in  a  body  can  be  ordinarily  distin- 
guished by  the  eye  only  when  the  body  is  partially 
decayed.  We  may  say  of  these  compounds  and  of 
similar  things  what  Democritus  said  very  well  of 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          197 

them,  namely  esse  opinione,  lege,  vofup.  Plato  had 
the  same  opinion  in  regard  to  all  that  is  purely 
material.  Our  mind  sees  or  conceives  of  certain 
true  substances  which  have  certain  modes.  These 
modes  involve  relations  to  other  substances  when- 
ever the  mind  finds  occasion  to  join  them  in  thought 
and  to  make  one  name  stand  for  the  whole  assem- 
bly of  these  things,  which  name  shall  serve  as 
a  means  of  reasoning;  but  we  must  not  make  the 
mistake  of  thinking  that  they  are  substances  or 
veritably  real  beings.  This,  position  can  be  held 
only  by  those  who  go  no  farther  than  appearances, 
or  else  by  those  who  consider  as  realities  all  the 
abstractions  of  the  mind  and  who  conceive  number, 
time,  place,  motion,  form  and  sensible  quality  as 
so  many  beings  by  themselves.  I,  on  the  contrary, 
hold  that  philosophy  cannot  be  restored  in  a  better 
way  nor  better  reduced  to  precision  than  by  recog- 
nizing substances  or  complete  beings  endowed  with 
a  true  unity  in  which  different  states  succeed.  All 
the  rest  are  to  be  considered  only  as  phenomena, 
abstractions  or  relations. 

Nothing  will  ever  be  found  fitted  to  constitute  a 
true  substance  out  of  several  beings  by  means  of 
aggregation;  for  example,  if  the  parts  which  fit 
together  for  a  common  design  are  more  appropriate 
to  constitute  a  true  substance  than  those  which  are 
in  contact,  all  the  officials  of  the  India  Company  in 
Holland  would  constitute  a  real  substance  better 
than  would  a  pile  of  stones.  But  such  a  common 
design — what  is  it  but  a  resemblance,  or  rather  an 
arrangement  of  actions  and  passions,  which  our 
mind  sees  in  different  things?  If  this  unity  by  con- 
tact should  be  preferred  as  the  most  reasonable 


198 


CORRESPONDENCE. 


hypothesis,  other  difficulties  would  be  found:  the 
parts  of  solid  bodies  are  perhaps  united  only  by  the 
pressure  of  surrounding  bodies  and  by  their  own 
pressure,  and  in  their  substance  they  may  have  no 
more  union  than  a  pile  of  sand  arena  sine  calce, 
Why  will  many  rings  linked  together  to  constitute 
a  chain  compose  more  of  a  true  substance  than  if 
they  had  openings  by  means  of  which  they  could 
be  separated?  It  is  possible  that  the  links  of  a  chain 
should  not  touch  one  another  and  should  not  even 
be  interlinked  and  yet,  nevertheless,  unless  they 
were  taken  in  a  certain  particular  way  they  could 
not  be  separated,  as  in  the  accompanying  figure. 


Would  it  be  said  in  such  a  case  that  the  substance 
of  this  compound  is,  as  it  were,  in  suspense,  and 
depends  upon  the  future  cleverness  of  him  who 
wishes  to  separate  them?  These  are  all  fictions  of 
the  mind,  and  so  far  as  we  do  not  discern  what  is 
truly  a  complete  being,  or  indeed,  a  substance,  we 
shall  have  no  resting  place,  and  through  this  distinc- 
tion of  substances  alone  is  there  a  means  of  estab- 
lishing stable  and  real  principles. 

In  conclusion,  nothing  should  be  considered  cer- 
tain without  a  basis.  It  is  therefore  for  those  who 
speak  of  beings  and  substances  without  a  real  unity 
to  prove  that  there  is  more  reality  than  that  which 
has  just  been  spoken  of;  and  I  am  awaiting  that 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          199 

concept  of  a  substance  or  of  a  being  which  can 
include  all  those  things  and  in  accordance  with 
which,  parts  and  perhaps  even  dreams  may  some 
day  pretend  to  reality:  at  least  I  hope  that  precise 
limits  will  be  given  to  the  citizenship  rights  which 
are  being  granted  to  beings  formed  by  aggregation. 

I  have  treated  this  subject  at  length  so  that  you 
might  understand  not  only  my  positions  but  also  the 
reasons  which  have  compelled  me  to  assume  them. 
I  submit  them  to  your  judgment  whose  fairness  and 
exactness  I  know.  I  send  also  an  article  in  The 
News  of  the  Republic  of  Letters  which  you  may 
find  will  serve  as  a  reply  to  the  Abbe  Catelan.  I 
consider  him  an  able  man  after  what  you  have  said, 
but  what  he  has  written  against  M.  Huygens  and 
against  me,  makes  it  clear  that  he  goes  a  little  too 
fast.  We  shall  see  what  he  will  do  now.  I  am 
delighted  to  learn  of  the  good  condition  of  your 
health  ;  I  desire  its  continuation  with  all  the  zeal 
and  all  the  passion  which  makes  me,  M.,  etc. 

P.  S. — I  reserve  for  another  time  certain  subjects 
which  you  have  touched  upon  in  your  letter. 


XVIII 

Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

April  30,  1687. 

Monseigneur: 

I  hope  that  your  Serene  Highness  will  receive  the 
book  which  was  delayed  so  long;  I  looked  for  it 
myself  at  Wolfenbuttel  in  order  that  you  might  have 
it  again  since  you  were  laying  the  blame  on  me. 
I  have  taken  the  liberty  to  add  a  letter  and  some 


200  CORRESPONDENCE. 

documents  for  M.  Arnaud.  I  have  some  hope  that 
when  he  shall  have  read  them,  his  penetration  and 
his  sincerity  will,  perhaps,  enable  him  to  approve 
entirely  of  that  which  at  the  beginning  seemed 
strange  to  him,  because  since  he  has  modified  his 
position  after  having  seen  my  first  explanation,  per- 
haps he  will  come  to  approbation  after  having  seen 
this  last  one  which,  in  my  opinion,  clearly  does 
away  with  all  the  difficulties  that  he  said  still 
troubled  him.  However  that  may  be,  I  shall  be 
content  if  he  decides,  at  least,  that  these  opinions, 
even  though  they  may  be  very  false,  entail  nothing 
directly  contrary  to  the  definitions  of  the  Church 
and  that  consequently  they  are  tolerable  even  in  a 
Roman  Catholic.  For  your  Serene  Highness 
knows,  better  than  1  can  tell,  that  there  are  toler- 
able errors,  and  that  there  are  even  errors  whose 
consequences  are  believed  to  destroy  the  articles  of 
faith,  and  yet,  nevertheless,  neither  these  errors 
nor  those  who  hold  them  are  condemned  because 
the  consequences  are  not  approved  of.  For  exam- 
ple, the  Thomists  hold  that  the  hypothesis  of  the 
Molinists  destroys  the  perfection  of  God;  while,  on 
the  other  hand,  the  Molinists  think  that  the  predeter- 
mination of  the  former  destroys  the  freedom  of 
man;  nevertheless,  since  the  Church  has  not  yet 
come  to  any  conclusion  upon  the  matter,  neither  the 
former  nor  the  latter  can  be  considered  as  heretics 
nor  their  opinions  as  heresies.  I  think  the  same 
can  be  said  of  my  proposition,  and  for  many  reasons 
I  should  like  to  know  if  M.  Arnaud  does  not  him- 
self now  acknowledge  their  harmlessness.  He  is 
very  busy  and  his  time  is  too  valuable  for  me  to 
pretend  that  he  should  employ  it  in  discussing  a 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          2OI 

matter  regarding  the  truth  or  falsehood  of  an  opin- 
ion; but  it  is  easy  for  him  to  decide  upon  its  tolera- 
bility,  since  it  is  merely  a  question  of  knowing 
whether  they  are  contrary  to  certain  definitions  of 
the  Church. 


XIX 

Leibniz  to  A  rnauld. 

August  ist,  1687. 

I  have  learned  with  much  pleasure  that  his  Serene 
Highness,  Count  Ernst,  has  seen  and  found  you  in 
good  health.  I  hope  with  all  my  heart  that  I  shall 
have  such  news  frequently,  and  that  the  body  will 
feel  as  little  the  effects  of  age  as  has  the  mind,  whose 
energy  still  manifests  itself.  I  have  myself  appre- 
ciated this  energy,  and  I  confess  that  I  know  no  one 
from  whom  I  look  for  a  judgment  upon  my  medita- 
tions more  stable,  more  penetrating,  and  also  more 
sincere  than  from  you. 

I  do  not  wish  to  trouble  you,  but  the  material  of 
the  later  letters  being  of  an  importance  second 
only  to  that  of  religion  and  having  great  affinities 
with  it,  I  confess  that  I  should  like  to  be  able  to 
enjoy  once  more  your  enlightenment  and  at  least 
to  learn  your  opinion  in  regard  to  my  last  explana- 
tions ;  for  if  you  find  in  them  an  appearance  of 
reason,  I  shall  be  confirmed,  but  if  you  find  anything 
to  say  against  them  I  shall  advance  more  cautiously 
and  shall  be  obliged  to  examine  some  day  the  whole 
subject  anew. 

In  place  of  M.  Catelan  it  was  the  Rev.  Father  Male- 
branche  who  replied  a  short  time  ago  in  The  News 


202  CORRESPONDENCE. 

of  the  Republic  of  Letters  to  the  objection  which  I 
had  put  forward.  He  seems  to  realize  that  cer- 
tain of  the  laws  of  nature  or  principles  of  motion 
which  he  advanced  would  be  difficult  to  maintain  ; 
but  he  thought  this  was  because  he  had  based  them 
on  the  assumption  of  absolute  hardness  which  is 
not  found  in  nature,  while  I  think  that  if  absolute 
hardness  could  be  found  in  nature  these  laws  would 
still  be  untenable.  It  is  a  defect  in  the  reasoning 
of  Descartes  and  his  followers  not  to  have  consid- 
ered that  everything  that  is  said  of  motion,  of  ine- 
quality, and  of  elasticity,  should  also  be  true  if 
things  are  supposed  to  be  infinitely  small.  In  this 
case  motion  (infinitely  small)  becomes  rest,  inequal- 
ity (infinitely  small)  becomes  equality , and  elasticity 
(infinitely  prompt)  is  nothing  else  than  extreme  hard- 
ness; somewhat  as  everything  which  geometers 
demonstrate  regarding  an  ellipse  proves  true  of  a 
parabola,  when  conceived  as  an  ellipse  with  its  second 
focus  infinitely  distant.  It  is  a  remarkable  thing  to 
see  that  almost  all  Descartes'  laws  of  motion  conflict 
with  this  principle,  which  I  hold  to  be  quite  as  infal- 
lible in  physics  as  it  is  in  geometry,  because  the 
author  of  things  acts  as  a  perfect  geometer.  If  I 
make  any  reply  to  Father  Malebranche  it  will  be 
principally  in  order  to  point  out  the  above  men- 
tioned principle,  which  is  x>f  great  utility  and  which 
has  not  as  yet  been  generally  considered,  so  far  as 
I  know. 

But  I  am  detaining  you  too  long  and  this  matter 
is  not  worthy  of  your  attention,     I  am,  etc., 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFKLS.          203 

XX 

Arnauld  to  Leibniz. 

August  28th,  1687. 

I  must  begin  by  making  excuses  for  replying  so 
late  to  your  letter  of  April  3d.  Since  then  I  have 
had  various  illnesses  and  various  occupations  and 
beside  it  is  a  little  hard  for  me  to  apply  myself  to 
such  abstract  things;  1  therefore  ask  for  your  con- 
sideration if  I  give  rather  briefly  my  opinion  about 
the  new  points  in  your  last  letter. 

1.  I   have  no  clear  idea  what  you  mean  by  the 
word  express  when  you  say  that  "our  soul  expresses 
more  distinctly,  other  things  being  equal,  that  which 
pertains  to  its  own  body,  since  it  expresses  even  all 
the  universe  in  a  certain  sense."     For  if  by  this 
expression  you  mean  a  certain  thought  or  a  certain 
knowledge,   I  cannot  agree  that  my  soul  has  more 
thought  and  knowledge  regarding  the  movement  of 
the    lymph  in  the  lymphatic  ducts  than  regarding 
the  movement  of  the  satellites  of  Saturn;  if  what 
you  call  expression  is  neither  thought  nor  knowl- 
edge, I  do  not  know  what  it  is.    Therefore  it  cannot 
be  of  service  in  solving  the  difficulty  which  I  raised; 
namely,   how  my  soul  can  have  a  feeling  of  pain 
when  I  am  pricked  during  my  sleep;  since  for  this 
it  would  have  to  know  that  some  one  were  pricking 
me,  while  in  fact  it  obtains  this  knowledge  only  by 
the  pain  which  it  feels. 

2.  In  regard  to  the   following   reasoning  in  the 
philosophy  of  occasional  causes:  "my  hand  moves 
as  soon  as  I  wish  it;  now  it  is  not  my  soul  which  is 
the  real  cause  of  this  motion,  neither  is  it  the  body, 
therefore  it  is  God";  you  say  that  this  supposes  that 


204  CORRESPONDENCE. 

a  body  cannot  move  itself.  Your  thought,  how- 
ever, is  that  it  can,  and  you  hold  that  whatever  there 
is  of  reality,  in  the  state  which  is  called  motion, 
proceeds  quite  as  much  from  the  corporeal  sub- 
stance itself,  as  the  thought  and  the  will  proceeds 
from  the  mind. 

This  is  what  seems  to  me  very  hard  to  understand, 
that  a  body  which  has  no  motion  can  give  itself 
motion.  And  if  this  is  admitted,  one  of  the  proofs  for 
the  being  of  God  is  destroyed;  namely,  the  neces- 
sity for  a  first  mover. 

Moreover,  if  a  body  could  give  motion  to  itself, 
it  would  not  result  in  my  hand's  moving  itself  every 
time  that  I  wished  it;  for,  being  without  knowledge, 
how  would  it  know  when  I  wished  it  to  move 
itself. 

3.  I  have  more  to  say  in  regard  to  the  indivisible 
and  indestructible  substantial  forms  which  you  think 
should  be  admitted  in  the  case  of  all  animals  and 
perhaps  even  in  the  case  of  plants,  because  other- 
wise matter  (which  you  consider  as  neither  com- 
posed of  atoms  nor  of  mathematical  points,  but  to 
be  divisible  to  infinity)  would  not  be  a  unutn perse 
but  only  an  aggregotum  per  accidens. 

(i).  I  replied  to  you  that  perhaps  it  is  an  essential 
of  matter,  which  is  the  most  imperfect  of  all  beings, 
not  to  have  any  true  and  proper  unity,  just  as  St. 
Augustine  thought,  that  is,  to  be  plura  entia  and 
not  properly  unum  ens;  and  that  this  is  no  more 
incomprehensible  than  is  the  infinite  divisibility  of 
matter,  which  you  admit. 

But  you  replied  that  this  cannot  be  so,  because 
there  can  be  no  plura  entia  where  there  is  no  unum 
ens. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.         205 

But  how  can  you  employ  this  argument,  which  M. 
Cordemoy  perhaps  might  have  thought  true,  but 
which,  according  to  you,  must  be  necessarily  false, 
since,  excepting  animated  beings,  which  do  not 
form  one  hundred  thousand  thousandth  part,  all  the 
rest  must,  in  your  opinion,  be  without  substantial 
forms,  merely  plura  entia  and  not  properly  unum 
ens?  It  is,  therefore,  not  impossible  that  there 
should  be  plura  entia  even  where  there  is  properly 
no  unum  ens. 

(2).  I  do  not  see  that  your  substantial  forms  can 
remedy  this  difficulty,  for  the  attribute  of  the  ens  which 
is  called  unum,  taken  as  you  take  it,  strictly  meta- 
physically, must  be  essential  and  intrinsic  to  what 
is  called  the  unum  ens.  Therefore,  if  a  particle  of 
matter  is  not  a  unum  ens  but  plura  entia,  I  do  not 
see  how  a  substantial  form,  which  being  really  dis- 
tinguished from  it,  could  only  give  it  an  extrinsic 
property — how  this  substantial  form  could  make  it 
cease  being  a  plura  entia  and  should  make  it  a  unum 
ens  by  an  intrinsic  property.  I  understand  easily  that 
this  would  give  us  a  reason  for  calling  it  unum  ens, 
if  we  did  not  take  the  word  unum  in  this  meta- 
physical strictness.  Substantial  forms,  however,  are 
not  called  for  in  order  to  be  able  to  give  the  name 
one  to  an  infinity  of  inanimate  bodies,  because,  is  it 
not  correct  usage  to  say  that  the  sun  is  one,  that  the 
earth  which  we  inhabit  is  one,  etc?  It  is  not  evident, 
therefore,  that  there  is  any  necessity  for  admitting 
these  substantial  forms  in  order  to  give  to  bodies  a 
true  unity,  which  they  would  not  otherwise  have. 

(3).  You  admit  these  substantial  forms  only  in 
animate  bodies.*  Now  there  are  no  animate  bodies 

*  Leibniz's  note:  "I  do  not  remember  having  said  that." 


2O6  CORRESPONDENCE. 

which  are  not  organized,  nor  are  there  any  organized 
bodies  which  are  not  plura  entia;  therefore  your 
substantial  forms,  far  from  preventing  bodies  to 
which  they  are  joined  from  being  plura  entia,  must 
themselves  become  plura  entia  in  order  that  they  may 
be  joined. 

(4).  I  have  no  clear  idea  of  these  substantial  forms 
or  souls  as  applied  to  brutes.  It  must  be  that  you 
regard  them  as  substances,  since  you  call  them  sub- 
stantial, and  since  you  say  that  only  substances  are 
truly  real  beings,  among  which  you  include  above  all 
these  substantial  forms.  Now  I  know  only  two  sorts 
of  substances,  bodies  and  minds,  and  it  is  for  those 
who  claim  that  there  are  others  to  show  me  them, 
according  to  the  maxim  with  which  you  conclude 
your  letter,  "that  nothing  should  be  considered  certain 
without  a  basis. ' '  Suppose  therefore  that  these  sub- 
stantial forms  are  either  bodily  or  mental;  if  they 
are  bodily  they  must  be  extended  and  consequently 
divisible  and  divisible  to  infinity;  hence  it  follows 
that  they  are  not  a  unum  ens  but  plura.  entia\  just  as 
are  the  physical  bodies  which  they  animate;  they 
are  not  therefore  able  to  impart  a  true  unity.  If, 
however,  the  subtantial  forms  are  mental,  their 
essence  will  be  to  think,  for  this  is  what  I  under- 
stand by  the  word  mind.  It  is  hard  for  me  to  under- 
stand how  an  oyster  thinks  or  a  worm  thinks;  and 
since  you  say  in  your  last  letter  that  you  are  not  sure 
but  that  plants  have  a  soul,  have  a  life  or  a  sub- 
stantial form,  it  must  be  you  are  not  sure  that  plants 
do  not  think,  because  their  substantial  forms,  if  they 
have  any,  not  being  corporeal  because  they  are  not 
extended,  must  be  mental,  that  is  to  say,  a  sub- 
stance which  thinks. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          207 

(5).  The  indestructibility  of  these  substantial 
forms  or  souls  in  brutes  appears  to  me  still  more 
untenable.  I  asked  you  what  became  of  the  souls 
of  these  brutes  when  they  died  or  when  they  were 
killed,  just  as  when  worms  were  burned  what  became 
of  their  souls.  You  reply  "that  they  remain  for 
each  worm  in  a  small  part  of  the  body  that  remains 
alive.  This  will  always  be  as  small  as  is  necessary 
to  serve  as  a  shelter  from  the  action  of  the  fire  which 
tears  to  pieces  or  which  destroys  the  bodies  of  these 
worms."  This  brings  you  to  say  that  "the  ancients 
were  mistaken  in  introducing  the  transmigration  of 
souls  in  place  of  the  transformation  of  the  same  ani- 
mal which  always  preserves  the  same  soul."  Noth- 
ing can  be  imagined  more  subtle  for  meeting  the 
difficulty  that  I  raised,  but  you  will  have  to  be  on 
your  guard,  M.,  against  what  I  am  about  to  say; 
when  a  silk  moth  casts  its  eggs  each  one  of  these 
eggs  in  your  opinion  has  the  soul  of  a  silk  worm, 
whence  it  happens  that  five  or  six  months  later  little 
silk  worms  hatch  out.  Now,  if  a  hundred  of  these 
silk  worms  had  been  burned  there  would  be,  in  your 
opinion,  a  hundred  souls  of  silk  worms  in  so  many 
little  particles  of  the  ashes;  but  on  the  one  hand  I 
do  not  know  any  one  whom  you  can  persuade  that 
each  silk  worm  after  having  been  burned  remains 
the  same  animal  preserving  the  same  soul  joined 
now  to  a  speck  of  ashes  which  was  formerly  a  little 
portion  of  its  own  body;  and,  on  the  other  hand,  if 
this  were  so,  why  is  no  silk  worm  born  out  of  these 
specks  of  ashes  as  they  are  born  out  of  the  eggs? 

(6).  This  difficulty  appears  greater  in  the  case  of 
animals,  where  it  is  known  certainly  that  they  can- 
not be  born  except  through  the  alliance  of  two 


208  CORRESPONDENCE, 

sexes;  I  ask,  for  example,  what  became  of  the  soul 
of  the  ram  which  Abraham  offered  in  place  of  Isaac 
and  which  he  burned?  You  will  not  say  that  it  passed 
into  the  foetus  of  another  ram,  for  this  would  be  the 
metempsychosis  which  you  condemn;  but  you  reply 
that  it  remained  in  a  particle  of  the  body  of  this  ram 
reduced  to  ashes  and  that  therefore  it  is  only  the 
transformation  of  the  same  animal  which  has  always 
preserved  the  same  soul.  This  could  be  said  with 
some  appearance  of  truth  in  your  hypothesis  of  the 
substantial  forms  of  a  caterpillar  which  becomes  a 
butterfly,  because  the  butterfly  is  an  organized  body 
quite  as  much  as  is  the  caterpillar,  and  therefore  it 
is  an  animal  which  can  be  considered  the  same  as 
the  caterpillar  because  it  preserves  many  of  the 
parts  of  the  caterpillar  without  any  change,  and  the 
other  parts  have  changed  only  the  forms.  But  this 
part  of  the  ram,  reduced  to  ashes,  in  which  the  soul 
of  the  ram  has  taken  refuge,  not -being  organized, 
cannot  be  taken  for  an  animal,  and  therefore  the 
soul  of  the  ram  which  is  joined  to  it,  does  not  com- 
pose an  animal,  much  less  a  ram,  such  as  the  soul  of 
a  ram  should.  What  will  then  become  of  the  soul  of 
this  ram  in  this  cinder?  For  it  cannot  separate 
itself  away,  to  go  elsewhere,  since  this  would  be  a 
transmigration  of  the  soul,  that  you  have  con- 
demned. The  same  is  the  case  with  an  infinity  of 
other  souls  which  would  never  form  animals  because 
of  being  joined  to  particles  of  matter  not  organ- 
ized, but  which  invisible  could  become  organized 
according  to  laws  established  in  nature.  What  an 
infinity  of  monstrous  things  would  be  this  infinity 
of  souls  joined  to  bodies  which  cannot  become  ani- 
mated! 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS.          209 

Not  long  since  I  saw  what  Abbe  Catelan  replied 
to  your  answer  in  The  News  of  the  Republic  of  Let- 
ters for  the  month  of  June.  What  he  said  there 
seemed  very  clear  to  me,  perhaps  however,  he  did 
not  entirely  understand  your  thought;  therefore, 
I  am  awaiting  the  reply  which  you  will  make  to  him. 
I  am,  Monsieur, 

Your  very  humble  and  very  obedient  servant, 

A.  A. 

XXI 

A.   Arnauld  to  Count  Ernst  von  Hessen-Rheinfels. 

August  3 ist,  1687. 

Here,  M.,  is  the  reply  to  the  last  letter  which  M. 
Leibniz  sent  through  your  Serene  Highness  in  April 
last.  I  was  not  able  to  apply  myself  to  it  sooner  in 
order  to  reply  to  it.  I  beg  you  to  send  it  on  to  him 
because  I  do  not  know  his  traits.  If  you  will  look 
it  through  you  will  see  that  there  are  a  good  many 
very  strange  opinions  in  regard  to  physics  and  some 
which  appear  to  be  hardly  tenable,  but  I  have  tried 
to  tell  him  my  opinion  regarding  them  in  a  way 
which  should  not  wound  him;  it  would  be  better 
were  he  to  quit,  for  a  time  at  least,  these  kinds  of 
speculations,  in  order  to  apply  himself  to  the  most 
important  business  that  he  can  have,  which  is  the 
choice  of  the  true  religion  in  accordance  with  what 
he  wrote  to  your  Highness  a  few  years  ago.  There 
is  cause  for  fear  that  death  may  overtake  him  before 
he  has  taken  a  step  so  important  for  his  salvation. 
M.  Nicole's  book  against  Seigneur  Jurieu's  new 
ecclesiastical  system  has  just  been  printed.  We  are 
expecting  it  from  Paris  in  five  or  six  days.  I  will 


210  CORRESPONDENCE. 

send  you   a  copy   by  the    Cologne    stage  together 
with  certain  other  books  which  you  will  like  to  see. 

XXII 

Count  Ernst  von  Hessen-Rhemfels  to  Leibniz. 
My  dear  M.  Leibniz: 

There  is  reason  for  saying  what  M.  Arnauld  has 
said;  for  even  if  there  were  thousands  among  the 
Protestants  who  did  not  know  their  right  hand  from 
their  left,  who,  in  comparison  with  the  savants, 
would  be  reputed  as  unthinking  brutes,  and  who 
adhered  only  materially  to  heresy,  certainly  this 
cannot  be  said  of  you  who  have  so  much  enlighten- 
ment, and  with  respect  to  whom,  if  there  had  never 
been  any  other  but  myself,  as  much  as  possible  has 
been  done  to  make  you  come  forth  from  the  Schis- 
matics and  to  represent  to  you  whatever  there  was 
to  be  represented.  To  mention  merely  one  out  of  a 
thousand  points;  do  you  believe  that  Christ  would 
have  so  constituted  his  Church  that  what  one  thought 
white  another  might  think  black,  and  that  he  would 
have  constituted  the  ecclesiastical  ministry  in  such 
a  contradictory  fashion  that  we  should  be  in  debate 
about  it  with  the  Protestants,  we  thinking  one  thing 
and  you  thinking  another?  For  example,  we  hold 
that  your  ministers  are  laymen  and  are  usurpers  in 
the  ministry.  I  do  not  know  what  you  may  think 
of  ours  who  are  so  opposed  to  yours  on  this  point. 
O,  my  dear  M.  Leibniz,  do  not  lose  thus  the  time 
of  grace  and  hodie  si  vocem  Domini  auderitis,  nolite 
obdurare  corda  vestra.  Christ  and  Belial  can  no  more 
agree  together  than  do  the  Catholics  and  Protest- 
ants, and  I  know  nothing  which  promises  your  sal- 
vation unless  you  become  a  Catholic. 


LEIBNIZ.       ARNAULD.        HESSEN-RHEINFELS.          211 

XXIII 

Leibniz  to  Arnauld. 

October  6,  1687. 

As  I  always  hold  in  high  esteem  your  criticism 
when  you  have  seen  the  point  at  issue,  I  will  try  this 
time  so  to  write  that  the  positions  which  I  hold  as 
important  and  almost  as  certain,  may  appear  to  you, 
if  not  certain,  at  least  as  entertainable;  for  it  does  not 
seem  to  me  at  all  difficult  to  answer  the  doubts  which 
you  still  have,  and  which,  in  my  opinion,  result  only 
because  a  person,  however  able  he  may  be,  when  he 
has  his  mind  made  up  and  is  otherwise  diverted, 
has  difficulty  at  first  in  entering  into  a  new  line  of 
thought  upon  an  abstract  subject,  where  neither 
figures  nor  models  nor  illustrations  can  assist  him. 

I  have  said  that  the  soul  naturally  expresses  the 
whole  universe  in  a  particular  sense  and  according 
to  the  relation  which  other  bodies  have  to  its  own; 
consequently,  as  it  expresses  most  directly  that 
which  belongs  to  the  parts  of  its  own  bodies,  it 
ought,  in  virtue  of  the  laws  of  relationship  which  are 
essential  to  it,  to  express  in  particular  certain 
unusual  changes  of  its  own  body;  for  instance,  that 
which  happens  when  it  feels  pain.  To  this  you 
reply  that  you  have  no  clear  idea  of  what  I  mean  by 
the  word  express;  that,  if  I  mean  by  it  a  thought, 
you  will  not  agree  that  the  soul  has  any  more 
thought  and  cognizance  of  the  movement  of  the 
lymph  in  the  lymphatic  ducts  than  of  the  move- 
ments of  the  satellites  of  Saturn.  If  I  mean,  how- 
ever, something  else,  you  say  you  do  not  know  what 
it  is,  and,  consequently  (supposing  that  I  were  not 
able  to  explain  it  distinctly),  this  word  would  be 


212  CORRESPONDENCE. 

of  no  service  in  letting  us  know  how  the  soul  can 
become  aware  of  the  feeling  of  pain,  since  it  would 
needs  be,  you  say,  that  it  already  knew  that  I  was 
being  pricked  instead  of  obtaining  this  knowledge 
only  by  the  pain  which  it  felt. 

In  reply  to  this  I  will  explain  this  word  which 
you  think  is  obscure,  and  I  will  apply  it  to  the  diffi- 
culty which  you  have  raised.  One  thing  expresses 
another,  in  my  use  of  the  term,  when  there  is  a  con- 
stant and  regulated  relation  between  what  can  be 
said  of  the  one  and  of  the  other.  It  is  thus  that  a 
projection  in  perspective  expresses  a  structure. 
Expression  is  common  to  all  forms,  and  is  a  class 
of  which  ordinary  perception,  animal  feeling  and 
intellectual  knowledge  are  species.  In  ordinary 
perception  and  in  feeling  it  is  enough  that  what  is 
divisible  and  material  and  what  is  found  common  to 
several  beings  should  be  expressed  or  represented  in 
a  single  indivisible  being,  or  in  the  substance  which 
is  endowed  with  a  true  unity.  We  cannot  at  all 
doubt  the  possibility  of  such  a  representation  of 
several  things  in  a  single  one,  since  our  own  souls 
furnish  us  examples;  this  representation,  however, 
is  accompanied  by  consciousness  in  a  rational  soul 
and  becomes  then  what  is  called  thought. 

Now,  such  expression  is  found  everywhere,  because 
all  substances  sympathize  with  one  another  and 
receive  some  proportional  change  corresponding  to 
the  slightest  motion  which  occurs  in  the  whole  uni- 
verse. These  changes,  however,  may  be  more  or 
less  noticeable,  as  other  bodies  have  more  or  less 
relation  with  ours.  I  think  that  M.  Descartes  would 
have  agreed  with  this  himself,  for  he  would  doubt- 
less grant  that  because  of  the  continuity  and  divis- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          113 

ibility  of  all  matter  the  slightest  movement  would 
have  its  effect  upon  neighboring  bodies  and  conse- 
quently from  body  to  body  to  infinity,  but  in  dimin- 
ishing proportion.  Thus,  our  bodies  ought  to  be 
affected  in  some  sort  by  the  changes  of  all  others. 
Now,  to  all  the  movements  of  our  bodies  certain 
perceptions  or  thoughts  of  our  soul,  more  or  less  con- 
fused, correspond;  therefore,  the  soul  also  will  have 
some  thought  of  all  the  movements  of  the  universe, 
and  in  my  opinion  every  other  soul  or  substance  will 
have  some  perception  or  expression  of  them.  It  is 
tfue  that  we  do  not  distinctly  perceive  all  the  move- 
ments in  our  body,  as  for  example  the  movement  of 
the  lymph, but  to  use  an  example  which  I  have  already 
employed,  it  is  somewhat  in  the  same  way  that  I 
must  have  some  perception  of  the  motion  of  every 
wave  upon  the  shore  so  that  I  may  perceive  what 
results  from  the  whole;  that  is  to  say,  that  great 
sound  which  is  heard  near  the  sea.  In  the  same  way 
we  feel  also  some  indistinct  result  from  all  the 
movements  which  go  on  within  us,  but,  being  accus- 
tomed to  this  internal  motion,  we  perceive  it  clearly 
and  noticeably  only  when  there  is  a  considerable 
change,  as  at  the  beginning  of  an  illness.  It  is  to 
be  desired  that  physicians  should  apply  themselves 
to  distinguish  more  exactly  these  kinds  of  confused 
feeling  which  we  have  within  our  bodies.  Now, 
since  we  perceive  other  bodies  only  by  the  relation 
which  they  have  to  our  own,  I  had  reason  for  saying 
that  the  soul  expresses  better  what  belongs  to  its 
own  body  and  knows  the  satellites  of  Jupiter  and  of 
Saturn  only  in  accordance  with  a  motion  which  is 
produced  within  the  eye.  In  all  this  I  think  the 
Cartesians  would  argee  with  me,  excepting  that  I  sup- 


314  CORRESPONDENCE. 

pose  that  there  are  around  us  other  souls  beside  our 
own  to  which  I  attribute  a  lower  expression  or  percep- 
tion than  thought.  For  the  Cartesians  deny  feelings  to 
animals  and  do  not  admit  any  substantial  forms  out- 
side of  men.  This  does  not  at  all  affect  our  question 
here  regarding  the  cause  of  pain.  We  have  now  to 
ask  how  the  soul  perceives  the  movements  of  its 
body,  since  there  seems  to  be  no  way  of  explaining 
by  what  means  the  action  of  an  extended  mass  may  be 
transmitted  to  an  indivisible  being.  Most  Cartesians 
confess  that  they  can  give  no  reason  for  this  union; 
the  authors  of  the  hypothesis  of  occasional  causes 
think  that  it  is  a  nodus  vindice  dignus,  cut  Deus  ex 
machina  intervenire  debeat,  a  knot  worthy  of  such 
an  extricator  that  God  must  intervene  to  solve  it. 
For  my  part,  I  explain  it  in  a  natural  way.  From 
the  concept  of  substance  or  of  complete  being  in  gen- 
eral, where  the  present  state  is  always  a  natural 
consequence  of  the  preceding  state,  it  follows  that 
the  nature  of  every  singular  substance  and  conse- 
quently of  every  singular  soul  is  to  express  the  uni- 
verse. From  the  start  it  was  created  in  such  a  way 
that  in  virtue  of  the  laws  of  its  own  nature  it  is 
obliged  to  agree  with  whatever  takes  place  in  bodies, 
and  particularly  in  its  own.  There  is  no  cause  for 
astonishment  therefore,  that  it  is  of  the  nature  of 
the  soul  to  represent  to  itself  a  pricking  sensation 
when  its  body  is  pricked:  in  order  to  explain  this 
matter  let  us  put  on  opposite  sides: 

State  of  the  body  at  the  State  of  the  soul  at  mo- 
moment  A.  ment  A. 

State  of  the  body  at  the  State  of  the  soul  at  the 

succeeding  moment  B  (prick-  moment  B  (pain), 
ing). 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          215 

Just  as  the  state  of  the  body  at  the  moment  B 
follows  the  state  of  the  body  at  the  moment  A,  »in 
the  same  way  the  state  B  of  the  soul  is  a  conse- 
quence of  the  preceding  state  A  of  the  same  soul, 
according  to  the  concept  of  substance  in  general. 
Now,  the  states  of  the  soul  are  naturally  and  essen- 
tially expressions  of  the  corresponding  states  of  the 
world,  and  particularly  of  the  bodies  which  belong 
to  them;  therefore,  since  the  pricking  constitutes 
a  part  of  the  condition  of  the  body  at  the  moment 
B,  the  representation  or  expression  of  the  pricking, 
which  is  the  pain,  will  also  form  a  part  of  the  state 
of  the  soul  at  moment  B;  because,  as  one  motion  fol- 
lows from  another  motion,  so  one  representation  in 
a  substance,  whose  nature  it  is  to  be  representative, 
follows  from  another  repesentation.  Accordingly  the 
soul  must  needs  perceive  the  pricking  when  the 
laws  of  correspondency  require  it  to  express  more 
distinctly  some  extraordinary  change  in  the  parts  of 
its  body.  It  is  true  that  the  soul  does  not  always 
distinctly  perceive  the  causes  of  the  pricking  and  of 
its  future  pain,  when  they  are  still  concealed  in  the 
representation  of  the  state  A,  as  when  one  is  asleep 
or  for  some  other  reason  does  not  see  the  pin 
approaching.  This  is,  however,  because,  at  such  a 
time,  the  motion  of  the  pin  makes  too  little  impres- 
sion and  although  we  are  already  affected  in  some 
sort  by  all  the  motions  and  representations  in  our 
soul,  and  though  we  have  thus  in  us  the  representa- 
tion or  expression  of  the  causes  of  the  pricking,  and 
consequently  the  cause  of  the  representation  of  the 
same  pricking,  that  is  to  say,  the  cause  of  the  pain, 
we  are  yet  not  able  to  separate  them  out  from  all  the 
other  thoughts  and  movements  excepting  when  they 


2l6  CORRESPONDENCE. 

become  quite  considerable.  Our  soul  notices  only 
more  special  phenomena,  which  are  distinguishable 
from  others,  never  thinking  distinctly  of  any  one 
when  the  thought  is  about  them  all  equally.  , 

In  accordance  with  this,  I  do  not  see  that  the 
slightest  shade  of  difficulty  can  be  found  in  this 
position,  unless  it  be  denied  that  God  can  create  sub- 
stances which  are  made  from  the  start  in  such  a  way 
that  by  virtue  of  their  own  natures  they  agree  in  the 
series  of  events  with  the  phenomena  of  all  the 
others.  Now,  there  are  no  plausible  grounds  for 
denying  this  possibility.  Mathematicians  represent 
the  movements  of  the  heavens  by  means  of  machines, 
(as  when 

Jura  poli  rerumgue  fidem  legesque  deorum 
Cuncta  Syracusius  transtulit  arte  senex, 

a  thing  which  we  can  do  much  better  to-day  than 
Archimedes  could  in  his  time),  and  why  cannot  God, 
who  infinitely  surpasses  these  mathematicians,  create 
from  the  very  start  representative  substances  in  such 
a  way  that  they  shall  express  by  their  own  laws,  in 
accordance  with  the  natural  changes  of  their 
thoughts  or  representations,  whatever  is  to  happen  to 
all  bodies.  This  appears  to  me  not  only  easy  to 
conceive,  but  also  worthy  of  God  and  of  the  beauty 
of  the  universe,  and  in  a  way  a  necessary  conception, 
since  all  substances  must  have  a  harmony  and  union 
among  themselves,  and  all  must  express  in  them- 
selves the  same  universe  and  the  universal  cause, 
which  is  the  will  of  their  Creator,  and  the  decrees  or 
laws  which  He  has  so  established  that  they  fit 
together  in  the  best  possible  way.  Furthermore,  this 
mutual  correspondence  of  different  substances  which 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          217 

are  not  able,  if  we  speak  with  metaphysical  strict- 
ness, to  act  one  upon  another,  and  which,  neverthe- 
less, agree  as  though  one  were  acting  upon  the 
other,  is  one  of  the  strongest  proofs  for  the  exist- 
ence of  God  or  of  a  common  cause  which  each 
effect  must  always  express  according  to  its  point  of 
view  and  its  capacity.  Otherwise  the  phenomena  of 
different  minds  would  not  agree  and  there  would  be 
as  many  systems  as  substances;  or  rather,  it  would 
be  a  pure  chance  if  they  at  times  agreed.  All  the 
conceptions  which  we  have  of  time  and  of  space  are 
based  upon  this  agreement.  But  I  should  never  fin- 
ish, were  I  to  explain  exhaustively  all  that  is  con- 
nected with  our  subject;  however,  I  prefer  to  be 
prolix  rather  than  not  to  express  myself  sufficiently. 
To  go  on  to  your  other  objections,  I  now  think 
that  you  will  see,  M.,  what  I  mean,  when  I  say  that 
a  corporeal  substance  gives  to  itself  its  own  motion, 
or,  rather,  whatever  there  is  of  reality  in  the  motion 
at  each  moment,  that  is,  the  derivative  force,  of 
which  it  is  a  consequence;  for,  every  preceding  state 
of  a  substance  is  a  consequence  of  its  preceding  state. 
It  is  true  that  a  body  which  has  no  motion  cannot 
give  itself  motion;  but  I  hold  that  there  are  no  such 
bodies.  (Also, strictly  speaking,bodies  are  not  pushed 
by  others  when  there  is  a  contact,  but  it  is  by  their 
own  motion  or  by  the  internal  spring,  which  again  is 
a  motion  of  the  internal  parts.  Every  corporeal 
mass,  large  or  small,  has  already  in  it  all  the  force 
that  it  will  ever  acquire,  the  contact  with  other 
bodies  gives  it  only  the  determination,  or,  better,  this 
determination  takes  place  only  at  the  time  that  the 
contact  does).  You  will  say  that  God  can  reduce  a 
body  to  a  state  of  perfect  repose;  I  reply,  however, 


2  1 8  CORRESPONDENCE. 

that  God  can  also  reduce  it  to  nothing,  and  that  this 
body,  deprived  of  action  and  of  passion,  need  not 
be  considered  a  substance;  at  least,  it  is  enough  if  I 
say  that  when  God  ever  reduces  a  certain  body  to 
perfect  repose,  something  that  can  happen  only  by  a 
miracle,  he  would  require  a  new  miracle  in  order  to 
restore  any  motion  to  it.  You  see  that  my  opinion 
confirms  rather  than  destroys  the  proof  of  a  prime 
mover:  a  reason  must  always  be  given  for  the  com- 
mencement of  the  motion  and  for  the  laws  and  the 
agreement  of  the  motions  among  themselves,  and 
this  can  never  be  done  without  having  recourse  to 
God.  Furthermore,  my  hand  does  not  move  because 
I  wish  it  for  it  would  be  in  vain,  unless  I  had  a 
miraculous  faith,  for  me  to  wish  the  mountain  to 
move,  and  in  the  case  of  my  hand  I  should  not  be 
able  to  wish  its  moving  with  success  unless  it  were 
exactly  at  that  moment  that  the  muscles  of  my  hand 
made  the  necessary  contraction  for  this  effect;  so 
much  the  more  must  what  I  suffer  agree  with  the 
changes  of  my  body.  The  one  always  accompanies 
the  other  in  virtue  of  the  correspondence  which  I 
established  above;  each  one,  however,  has  its  cause 
immediately  in  itself. 

I  come  to  the  point  regarding  the  forms  or  the 
souls  which  I  consider  to  be  indivisible  and  inde- 
structible. I  am  not  the  first  one  to  hold  this  opin- 
ion. Parmenides,  of  whom  Plato  speaks  with 
respect,  as  well  as  Melissus,  held  that  there  was 
neither  generation  nor  corruption  except  in  appear- 
ance. Aristotle  takes  the  same  position  in  Book  3, 
De  ccelo,  chapter  2,  and  the  author  of  De  di&ta, 
Book  I.,  which  is  attributed  to  Hippocrates,  says 
expressly  that  an  animal  cannot  be  born  wholly  as  a 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          219 

new  animal  nor  entirely  destroyed.  Albertus 
Magnus  and  John  Bacon  seem  to  have  thought  that 
the  substantial  forms  were  already  concealed  in  mat- 
ter from  all  time;  Fernel  has  them  descend  from 
heaven,  to  say  nothing  of  those  who  derive  them 
from  the  soul  of  the  world.  These  have  all  seen  a 
part  of  the  truth,  but  they  have  not  developed  it. 
Most  of  them  believed  in  the  transmigration  and 
others  in  the  traduction  of  souls,  instead  of  think- 
ing of  the  transmigration  and  transformation  of  an 
animal  already  formed.  Others,  not  being  able  to 
explain  the  origin  of  the  forms,  have  said  that  they 
begin  by  a  true  creation.  Such  a  creation  in  time  I 
admit  only  in  the  case  of  reasoning  souls,  and  hold 
that  all  the  forms  which  do  not  think  were  created 
at  the  same  time  tha/  the  world  was.  But  they 
believe  that  this  creation  takes  place  all  the  time 
whenever  the  smallest  worm  is  born.  Philoponus, 
an  ancient  commentator  upon  Aristotle,  in  his  book 
against  Proclus,  and  Gabriel  Biel  seem  to  have  been 
of  this  opinion.  I  think  that  St.  Thomas  considered 
the  souls  of  beasts  as  indivisible.  Our  Cartesians  go 
much  further  when  they  say  that  every  soul  and 
every  true  substantial  form  must  be  indestructible 
and  ingenerable.  This  is  why  they  refused  souls  to 
beasts,  although  M.  Descartes,  in  a  letter  to  M. 
Morus,  says  that  he  is  not  certain  that  they  have  no 
souls.  Since  no  special  objection  is  made  to  those 
who  speak  of  perduring  atoms,  why  is  it  found 
strange  when  the  same  is  said  of  souls  to  which 
indivisibility  should  belong  by  their  very  nature, 
especially  because,  if  we  combine  the  position  of  the 
Cartesians  regarding  the  substance  and  the  soul, 
with  the  prevailing  opinion  regarding  the  souls  of 


230  CORRESPONDENCE. 

beasts,  the  indestructibility  necessarily  follows.  It 
will  be  difficult  to  overcome  this  opinion  which  has 
been  always  and  everywhere  received  and  which  has 
been  broadcast,  namely,  that  beasts  have  feelings. 
Now,  if  we  grant  that  they  have  souls,  what  I  hold 
regarding  the  indestructibility , of  the  souls  is  not 
only  necessary  according  to  the  Cartesians  but  it  is 
important  again  in  ethics  and  in  religion,  in  order 
to  controvert  a  dangerous  tenet  toward  which 
several  personages  of  intelligence  are  inclined  and 
which  the  Italian  philosophers,  who  are  disciples  of 
Averroes,  have  disseminated;  namely,  that  when  an 
animal  dies  the  particular  souls  return  to  the  soul  of 
the  world.  This  is  in  contradiction  to  my  demon- 
stration of  the  nature  of  the  individual  substance 
and  cannot  be  conceived  of  distinctly,  since  every 
individual  substance  must  always  subsist  apart  when 
once  it  has  commenced  its  being;  that  is  why  the 
truths  which  I  advance  are  so  important.  Those  who 
recognize  that  the  beasts  have  souls  should  approve 
of  them,  the  others  at  least  should  not  find  them 
strange. 

To  come,  however,  to  your  objections  regarding 
this  indestructibility: 

i.  I  have  held  that  we  must  admit  in  bodies  some- 
thing which  may  be  truly  a  single  being,  since  mat- 
ter or  extended  mass  in  itself  can  never  be  more 
than  plura  entia,  as  St.  Augustine,  following  Plato, 
has  very  truly  observed.  Now,  I  infer  that  there 
are  not  several  beings  where  there  is  not  even  one 
which  may  be  truly  a  being,  and  I  hold  that  every 
multitude  presupposes  unity;  to  this  you  make 
various  replies,  but  without  touching  the  argument 
itself,  which  is  unassailable;  you  use  only  arguments 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          221 

ad  hominem  and  from  inconveniences  which  would 
arise,  and  you  try  to  show  that  what  I  say  does  not 
solve  the  difficulty.  First  of  all,  you  are  aston- 
ished, M.,  how  I  am  able  to  make  use  of  this  reason, 
which  would  be  apparent  to  M.  Cordemoy  who  con- 
stitutes everything  out  of  atoms,  but  which,  from  my 
position,  as  you  think,  would  be  necessarily  false, 
since,  leaving  aside  animated  bodies  that  do  not  con- 
stitute the  hundred  thousand  thousandth  part  of  the 
universe,  all  the  others  would  necessarily  have  to 
be  plura  entia  and  the  difficulty  would  thus  come  up 
again.  From  this  I  see,  M.,that  I  did  not  explain 
myself  sufficiently  to  enable  you  to  grasp  my 
hypothesis,  for,  aside  from  the  fact  that  I  do  not 
remember  having  said  that  there  are  no  substantial 
forms  excepting  souls,  I  am  far  from  saying  that 
animated  bodies  constitute  only  a  small  proportion 
of  the  bodies  in  the  world;  for,  I  think  rather  that 
everything  is  full  of  animated  bodies,  and  in  my 
opinion  there  are  incomparably  more  souls  than  M. 
Cordemoy  has  atoms.  His  atoms  are  finite  in 
number,  while  I  hold  that  the  number  of  souls,  or  at 
least  of  forms,  is  wholly  infinite,  and  that  mat- 
ter being  divisible  without  end,  no  portion  can  be 
obtained  so  small  that  there  are  not  in  it  animated 
bodies,  or  at  least  such  as  are  endowed  with  a  prim- 
itive entelechy,  and  (if  you  will  permit  me  to  use 
the  word  life  so  generally),  with  the  vital  principle \ 
that  is  to  say,  with  corporeal  substances,  of  all  of 
which  it  may  be  said  in  general  that  they  are  alive. 
2.  As  regards  this  other  difficulty  which  you  made, 
M.,  namely  that  the  soul  joined  to  matter  does  not 
make  the  latter  truly  one,  since  the  matter  is  not 
really  one  in  itself,  and  since  the  soul,  as  you  think, 


322  CORRESPONDENCE. 

gives  it  only  an  extrinsic  character  I  reply  that 
it  is  the  animated  substance  to  which  this  matter 
belongs  that  is  really  a  being,  and  the  matter  which 
is  understood  as  the  mass  in  itself  is  only  a  pure 
phenomenon  or  appearance,  as  well-founded,  how- 
ever, as  is  space  and  time.  It  has  not  even  those 
precise  and  determined  qualities  which  can  enable 
it  to  pass  as  a  determined  being,  as  I  have  already 
indicated  in  what  precedes,  because  figure  itself, 
which  is  the  essence  of  a  limited  extended  mass,  is 
never,  strictly  speaking,  perfectly  determined  in  the 
state  of  nature  because  of  the  actually  infinite 
division  of  the  parts  of  matter:  there  is  never  a 
globe  without  inequalities,  never  a  straight  line 
without  an  intermingling  of  curves,  never  a  curve 
of  a  certain  finite  nature  without  an  intermixture 
of  some  other,  and  this  is  as  true  in  small  portions 
as  in  large,  so  that  far  from  the  figure  being  a  con- 
stitutive element  in  the  body,  it  is  not  a  quality 
at  all  real  and  determined  outside  of  the  thought. 
Never  can  an  exact  surface  be  assigned  to  any 
body  as  could  be  done  if  there  were  atoms;  I 
can  say  the  same  thing  of  size  and  of  motion, 
namely,  that  these  qualities  or  predicates  are  phe- 
nomena like  colors  and  sounds,  and  although  they 
involve  a  more  distinct  knowledge  they  cannot 
hold  up  under  a  final  analysis.  Consequently 
extended  mass,  when  considered  without  ente- 
lechies,  that  is,  as  consisting  only  in  those  qualities 
of  size  and  motion,  is  not  a  corporeal  substance 
but  a  wholly  pure  phenomenon  like  the  rainbow. 
It  has  been  also  recognized  by  philosophers  that  it 
is  the  substantial  form  which  gives  a  definite  being 
to  matter,  and  those  who  do  not  pay  attention  to 


LEIBNIZ.        ARNAULD.       HESSEN-RHEINFELS.          223 

that  point  will  never  get  out  of  the  labyrinth  of  the 
composition  of  the  continuum  if  they  once  enter: 
only  indivisible  substances  and  their  different  states 
are  absolutely  real.  This  Parminedes  and  Plato  and 
many  other  ancients  have  indeed  seen. 

However,  I  grant  that  the  word  one  can  be 
applied  to  a  gathering  together  of  inanimate  bodies 
although  no  substantial  form  unites  them,  just  as  I 
am  able  to  say  there  is  one  rainbow,  there  is  one 
herd.  But  this  is  a  unity,  phenomenal  or  of 
thought,  which  is  not  sufficient  for  the  reality  back 
of  the  phenomenon.  [If  we  take  as  the  matter  of 
the  corporeal  substance,  not  its  formless  mass  but  a 
secondary  matter  which  is  the  manifold  of  sub- 
stances whose  mass  constitutes  the  whole  body,  it 
can  be  said  that  these  substances  are  parts  of  this 
matter;  just  as  those  which  enter  into  our  body 
make  a  part  of  it.  It  is  the  same  with  other  cor- 
poreal substances  as  it  is  with  our  body,  which  is 
the  matter  and  the  soul,  which  is  the  form  of  our 
substance;  and  I  find  no  more  difficulty  in  this 
respect  than  is  found  in  the  case  of  man,  in  regard  to 
whom  all  are  agreed  upon  this  point.  The  diffi- 
culties which  come  up  in  these  subjects  are  due, 
among  other  reasons,  to  the  fact  that  we  have  not 
ordinarily  a  sufficiently  distinct  conception  of  the 
whole  and  of  the  parts,  because  essentially  the  part 
is  nothing  else  than  an  immediate  requisite  for  the 
whole  and  is,  in  a  way,  homogeneous  with  it;  there- 
fore, the  parts  can  constitute  a  whole,  whether  there 
is  a  real  unity  or  not.  It  is  true  that  the  whole, 
which  has  a  real  unity,  may  continue  as  the  same 
individual  in  the  strictest  sense  even  when  it  loses 
or  gains  parts  as  our  experience  shows  us.  In  these 


224  CORRESPONDENCE. 

cases  the  parts  are  immediate  requisites  only  pro 
tempore  but  if,  however,  we  understand  by  the  term 
matter  something  which  will  always  be  essential  to 
the  same  substance  we  might,  in  the  sense  of  certain 
of  the  Schoolmen,  understand  by  this  the  primitive 
passive  power  of  a  substance  and,  in  this  sense,  the 
matter  would  be  neither  extended  nor  divisible 
although  it  would  be  the  principle  of  divisibility  or 
of  that  which  stands  for  divisibility  in  the  substance. 
However,  I  do  not  wish  to  argue  regarding  the  use 
of  terms.] 

3.  You  object  that  I  admit  substantial  forms  only 
in  the  case  of  animated  bodies — a  position  which  I  do 
not,  however,  remember  to  have  taken.     Now,  you 
continue:  all  organized  bodies  being  plura  entia  the 
forms  or  souls  by  no  means  suffice  to  constitute  a 
being,  but  rather  there  must  be  several  beings  so 
that  the  body  can  be  animated.     I  reply  that  sup- 
posing there  is  a  soul  or  entelechy  in  beasts  or  in 
other  corporeal  substances,  we  must  reason  in  regard 
to  them  as  we  all  reason  regarding  man,  who  is  a 
being  endowed  with  a  real  unity;  his  soul  gives  him 
this  unity  although  the  mass  of  his  body  is  divided 
into  organs,   ducts,    humors,    spirits,    and   that   the 
parts  are  doubtless  full  of  an  infinity  of  other  cor- 
poreal substances  endowed  with  their  own  entele- 
chies.     As  this  third  objection  agrees  in  substance 
with  the  preceding  the  former  solution  will  suffice. 

4.  You  think  that  it  is  without  a  basis,  when  souls 
are  attributed  to  animals,  and  you  think  that  if  they 
had  souls  there  would  be  a  mind,  that  is  to  say,  a 
substance  which  thinks  since  we  know  only  bodies 
and  spirits  and  have  no  idea  of  any  other  substance; 
now,    that   an   oyster    thinks   or    a    worm    thinks, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          225 

it  is  difficult  to  believe.  This  objection  applies 
equally  to  all  those  who  are  not  Cartesians. 
Besides  the  fact,  however,  that  that  cannot  be 
entirely  unreasonable,  which  the  whole  human  race 
has  always  accepted,  namely  that  animals  have  feel- 
ings, I  think  I  have  shown  that  every  substance  is 
indivisible,  and  that  consequently  every  cor- 
poreal substance  must  have  a  soul  or  at  least  an 
entelechy  which  has  an  analogy  with  the  soul, 
because  otherwise  the  body  would  be  only  a  phe- 
nomenon. 

To  hold  that  every  substance  which  is  not  divisible 
(that  is  to  say,  in  my  opinion,  every  substance  in 
general),  is  a  mind  and  must  think,  appears  to  me 
incomparably  more  rash  and  more  destitute  of  basis 
than  the  conservation  of  forms.  We  know  only 
five  senses  and  a  certain  number  of  metals,  should 
we  conclude  that  there  are  none  other  in  the  world? 
It  seems  more  evident  that  nature,  which  loves 
variety,  has  produced  other  forms  than  those  which 
think.  If  I  am  able  to  prove  that  there  are  no  other 
figures  of  the  second  degree  than  those  found  in 
conic  sections  it  is  because  I  have  a  distinct  idea  of 
those  lines,  which  enables  me  to  reach  an  exact 
division;  as,  however,  we  have  no  distinct  idea  of 
thought  and  are  not  able  to  demonstrate  that  the 
concept  of  an  indivisible  substance  coincides  with 
that  of  a  substance  which  thinks,  we  have  no  cause 
for  being  certain  about  it.  I  agree  that  the  idea 
which  we  have  of  thought  is  clear  but  everything 
which  is  clear  is  not  distinct.  As  Father  Malebranche 
has  already  noticed,  it  is  only  by  internal  feeling 
that  we  recognize  thought,  we  can  recognize  by  feel- 
ing only  the  things  which  we  have  experienced,  and 


226  CORRESPONDENCE. 

as  we  have  not  experienced  the  functions  of  other 
forms  we  must  not  be  astonished  if  we  have  no  clear 
idea  of  them;  for,  we  ought  not  to  have  such  ideas 
even  if  it  were  granted  that  there  are  these  forms. 
It  is  a  mistake  to  try  to  employ  confused  ideas,  how- 
ever clear  they  may  be,  to  prove  that  something 
cannot  be;  and  when  I  pay  attention  to  distinct  ideas 
it  seems  that  we  can  conceive  that  phenomena  which 
vary  or  which  come  from  several  beings,  can  be 
expressed  or  represented  in  a  single  indivisible  being, 
and  this  is  sufficient  to  constitute  a  perception  with- 
out any  necessity  of  adding  thought  or  reflection 
to  this  representation.  I  would  wish  to  be  able 
to  explain  the  differences  or  the  degrees  of  the 
other  immaterial  expressions  which  are  without 
thought,  so  that  we  might  distinguish  corporeal  or 
living  substances  from  animals,  as  far  as  they  can 
be  distinguished.  I  have  not,  however,  meditated 
enough  about  the  above,  nor  sufficiently  examined 
the  things  in  nature  in  older  to  pass  judgment  upon 
the  forms  as  compared  with  their  organs  and  activ- 
ities. M.  Malpighi,  well  versed  in  important 
analogies  of  anatomy,  is  very  much  inclined  to 
think  that  plants  can  be  embraced  under  the  same 
class  with  animals  and  that  they  are  imperfect  ani- 
mals. 

5.  There  remains  for  me  only  to  satisfy  the  diffi- 
culties which  you  have  raised,  M.,  against  the  inde- 
structibility of  the  substantial  forms;  and,  first  of  all, 
I  am  surprised  that  you  find  this  point  strange  and 
untenable,  because,  according  to  your  own  position, 
all  those  who  assign  to  animals  a  soul  and  feeling 
ought  to  maintain  this  indestructibility.  These  sup- 
posed difficulties  are  only  prejudices  of  the  mind, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.  227 

which  may  detain  common  thinkers  but  which  have 
no  influence  upon  minds  capable  of  meditation.  I 
think  it  will  be  easy  to  satisfy  you  in  regard  to 
them.  Those  who  perceive  that  there  is  an 
infinity  of  small  animals  in  the  least  drop  of  water, 
as  the  experiments  of  M.  Leewenhoeck  have  shown, 
and  who  do  not  find  it  strange  that  matter  should  be 
entirely  filled  with  animated  substances,  will  not 
find  it  strange  either  that  there  should  be  some- 
thing animated  in  the  ashes  themselves,  and  that  fire 
can  transform  an  animal  and  reduce  it,  without,  how- 
ever, entirely  destroying  it.  That  which  can  be  said 
of  one  caterpillar  or  silk-worm  could  be  said  of  one 
hundred  or  one  thousand,  but  it  does  not  follow  that 
we  should  see  the  silk  worm  re-born  from  the  ashes. 
Perhaps  such  is  not  the  order  of  nature.  I  know 
that  many  assure  us  that  the  generative  powers 
remain  in  ashes  in  such  a  way  that  plants  can  be 
produced  from  them  but  I  do  not  wish  to  employ 
doubtful  experiments.  Whether  these  small  organ- 
ized bodies  produced  by  a  kind  of  contraction  from 
larger  bodies  that  have  become  destroyed,  are,  as  it 
seems  wholly  out  of  the  series  of  generation,  or 
whether  they  can  come  back  again  to  the  theater  of 
action  in  due  time,  is  something  which  I  am  unable  to 
determine.  These  are  secrets  of  nature  where  men 
must  acknowledge  their  ignorance. 

6.  It  is  only  apparently  and  as  a  result  of  the 
imagination  that  the  difficulty  seems  greater  with 
regard  to  the  larger  animals  which  are  born  only  by 
the  union  of  two  sexes.  This  is  apparently  not  less 
necessary  with  the  smallest  insects.  I  have  recently 
learned  that  M.  Leewenhoeck  holds  opinions  quite 
like  mine,  in  that  he  maintains  that  the  largest  ani- 


228  CORRESPONDENCE. 

mals  are  born  by  a  kind  of  transformation.  I  do 
not  dare  either  to  approve  or  to  reject  the  details  of 
his  opinion,  but  I  hold  it  as  true  in  general,  and  M. 
Swammerdam,  another  great  investigator  and 
anatomist,  says  that  he  also  has  leanings  toward 
that  opinion.  Now,  the  opinions  of  these  men  are 
far  more  important  in  such  matters  than  those  of 
many  others.  True  it  is,  I  do  not  see  that  they 
have  carried  out  their  opinions  so  far  as  to  say  that 
corruption,  and  death  itself,  is  also  a  transformation 
with  respect  to  the  living  beings  which  are  destitute 
of  a  reasonable  soul,  as  I  hold;  but  I  think  that  if 
they  were  informed  of  my  position  they  would  not 
find  it  absurd,  for  there  is  nothing  so  natural  as  to 
think  that  that  which  does  not  begin  does  not  perish 
either,  and  when  it  is  acknowledged  that  all  births 
are  only  growths  or  developments  of  an  animal 
already  formed,  it  is  easy  to  be  persuaded  that  decay 
or  death  is  nothing  else  than  the  diminution  or  the 
decrease  of  an  animal,  which,  nevertheless,  continnes 
to  exist  and  to  be  living  and  organized.  It  is  true 
that  it  is  not  as  easy  to  render  this  position  accept- 
able through  special  experiments  as  it  is  with 
respect  to  generation,  but  the  reason  for  this  is  evi- 
dent; it  is  because  generation  advances  from  phys- 
ical matter,  little  by  little,  so  that  we  have  time  to 
see  it,  but  death  goes  backward  too  much  by  a 
spring  and  at  once  returns  to  particles  too  small  for 
us,  because  death  occurs  usually  in  too  violent  a 
manner  for  us  to  be  able  to  follow  out  the  details  of 
this  retrogression.  Sleep,  however,  which  is  an 
image  of  death,  and  ecstacies,  and  the  condition  of 
the  silk  worm  in  its  cocoon,  which  might  pass  for  a 
death,  also  the  resuscitation  of  flies  quite  drowned, 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          229 

through  the  means  of  a  certain  dry  powder  that  may 
be  sprinkled  upon  them  (these  flies  remaining 
wholly  dead  if  they  are  left  without  any  assistance), 
and,  furthermore,  the  state  of  swallows,  which 
hibernate  in  the  reeds,  where  they  are  found  appar- 
ently dead,  and  the  experiences  of  men  who  die 
from  cold,  from  drowning  or  from  strangulation, 
whom  it  is  possible  to  bring  to  life  again  (in  regard 
to  which  not  long  since  a  careful  thinker  in  Germany 
wrote  a  treatise  where,  after  having  given  instances 
known  to  himself  personally,  he  exhorts  those  who 
have  to  do  with  such  persons,  to  make  more  efforts 
than  are  usually  made  to  revive  them,  and  he 
describes  the  proper  method) — all  these  things  serve 
to  confirm  my  position  that  these  different  states 
differ  only  in  degree,  and  if  we  have  not  the  means 
of  bringing  about  the  resuscitation  after  other  kinds 
of  death,  it  is  because  we  do  not  know  what  must 
be  done,  or,  even  if  we  should  know  what  must  be 
done,  our  hands  and  our  instruments  and  our 
remedies  would  not  be  successful,  above  all,  when 
the  dissolution  goes  at  once  into  too  minute  par- 
ticles. We  must  not,  therefore,  hold  to  the  notions 
which  common  people  may  have  regarding  death  or 
life,  when  there  are  both  analogies  and,  what  is 
better,  weighty  arguments  to  prove  the  contrary, 
for,  I  think,  I  have  sufficiently  shown  that  there 
must  be  entelechies  if  there  are  corporeal  substances, 
and  if  these  entelechies  or  souls  are  acknowl- 
edged, their  ingenerability  and  indestructibility 
must  be  recognized.  After  this,  it  is  incomparably 
more  reasonable  to  think  of  the  transformation  of 
animated  bodies  than  to  conceive  of  the  passage  of 
souls  from  one  body  to  another,  which  latter  opin- 


33°  CORRESPONDENCE. 

ion,  though  very  ancient,  seems  to  be  merely  a  form 
of  transformation  not  well  understood.  To  say  that 
the  souls  of  animals  remain  without  a  body  or  that 
they  remain  concealed  in  a  body  which  is  not  organ- 
ized, appears  less  natural  than  my  position.  Whether 
the  animal  resulting  from  the  diminution  of  the  body 
of  the  ram  which  Abraham  sacrificed  in  place  of  Isaac 
should  be  called  a  ram  is  only  a  question  of  names, 
very  much  as  would  be  the  question  whether  a  moth 
should  be  called  a  silkworm;  the  difficulty  which 
you  have  found,  M.,  in  regard  to  the  ram  reduced 
to  ashes  comes  only  because  I  did  not  sufficiently 
explain  myself.  You  suppose  that  no  organized 
body  remains  in  the  ashes  and  therefore  you  have  a 
right  to  say  that  it  would  be  a  monstrous  thing,  this 
infinity  of  souls  without  organized  bodies;  while  my 
position  is  that  in  the  state  of  nature  there  are  no 
souls  without  animated  bodies  and  no  animated 
bodies  without  organs  Neither  ashes  nor  any  other 
mass  appears  to  me  incapable  of  containing  organ- 
ized bodies. 

With  regard  to  spirits,  that  is  to  say,  substances 
which  think  and  which  are  able  to  recognize  God 
and  to  discover  eternal  truths,  I  hold  that  God  gov- 
erns them  according  to  laws  different  from  those 
with  which  he  governs  the  rest  of  substances;  for, 
while  all  the  forms  of  substances  express  the  whole 
universe,  it  can  be  said  that  animal  substances 
express  the  world  rather  than  God,  while  spirits 
express  God  rather  than  the  world.  God  governs 
animal  substances  according  to  the  material  laws  of 
force  and  of  the  transfer  of  motion,  but  spirits, 
according  to  spiritual  laws  of  justice,  of  which  the 
others  are  incapable.  It  is  for  this  reason  that  ani- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          231 

mal  substances  can  be  called  material,  because  the 
economy  which  God  observes  with  regard  to  them 
is  that  of  a  worker  or  of  a  machinist,  but  with  regard 
to  spirits  God  performs  the  functions  of  a  Prince  or 
of  a  Legislator,  which  is  infinitely  higher;  with 
regard  to  material  substances,  God  is  only  what  he 
is  with  regard  to  everything,  namely,  the  universal 
author  of  beings.  He  assumes,  however,  another 
aspect  with  regard  to  spirits  who  conceive  of  him  as 
endowed  with  will  and  with  moral  qualities; 
because  he  is,  himself,  a  spirit  and,  like  one  among 
us,  to  the  point  of  entering  with  us  into  a  social 
relation,  where  he  is  the  head.  It  is  this  universal 
society  or  republic  of  spirits  under  this  sovereign 
monarch  which  is  the  noblest  part  of  the  universe, 
composed  of  so  many  little  gods  under  this  one 
great  God;  for,  it  can  be  said  that  created  spirits 
differ  from  God  only  in  degree,  only  as  the  finite 
differs  from  the  infinite,  and  it  can  be  truly  said  that 
the  whole  universe  has  been  made  only  to  con- 
tribute to  the  beautifying  and  to  the  happiness  of 
this  city  of  God.  This  is  why  everything  is  so  con- 
structed that  the  laws  of  force  or  the  purely  material 
laws  work  together  in  the  whole  universe  to  carry 
out  the  laws  of  justice  or  of  love,  so  that  nothing 
will  be  able  to  injure  the  souls  that  are  in  the  hands, 
of  God,  and  so  that  everything  should  result  for 
the  greatest  good  of  those  who  love  him;  this  is 
why,  furthermore,  it  must  be  that  spirits  keep  their 
personalities  and  their  moral  qualities  so  that  the 
city  of  God  shall  lose  no  member  and  they  must  in 
particular  preserve  some  sort  of  memory  or  con- 
sciousness or  the  power  to  know  what  they  are,  upon 
which  depends  all  their  morality,  penalties  and 


23»  CORRESPONDENCE. 

chastisements.  Consequently,  they  must  be  exempt 
from  those  transformations  of  the  universe  which 
would  render  them  unrecognizable  to  themselves 
and,  morally  speaking,  would  make  another  person 
of  them.  For  animal  substances,  however,  it  is 
enough  if  they  remain  as  the  same  individual  in  the 
metaphysical  sense,  while  they  are  subjected  to  all 
imaginable  changes  because  they  are  without  con- 
science or  reflection. 

As  far  as  the  particulars  of  this  condition  of  the 
human  soul  after  death  are  concerned  and  in  what 
way  it  is  exempted  from  the  transformation  of  things, 
revelation  alone  can  give  us  particular  instruction; 
the  jurisdiction  of  the  reason  does  not  extend  so  far. 
Perhaps  an  objection  may  be  made  to  my  position 
when  I  say  that  God  has  given  souls  to  all  natural 
machines  which  are  capable  of  them,  because  the 
souls  do  not  interfere  with  one  another  and  do  not 
occupy  any  position;  and  that  it  is  possible  to 
assign  to  them  as  much  perfection  as  they  are  able 
to  have,  since  God  has  made  everything  in  the  most 
perfect  possible  manner;  "there  is  no  more  a 
vacuum  of  forms  than  of  bodies."  It  might  be  said 
that,  by  the  same  reasoning,  God  should  give  reason- 
ing souls  or  souls  capable  of  reflection  to  all  ani- 
mated substances.  But  I  reply  that  laws  superior  to 
the  laws  of  material  nature  are  opposed  to  this,  that 
is  to  say,  the  laws  of  justice,  because  the  order  of 
the  universe  would  not  permit  justice  to  be  observed 
toward  all,  and  it  would  have  to  be,  therefore,  that 
at  least  no  injustice  should  be  done  them;  that  is 
why  they  have  been  made  incapable  of  reflection  or 
consciousness,  and  consequently,  not  susceptible  of 
happiness  and  unhappiness. 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          233 

Finally,  to  recapitulate  my  position  in  a  few 
words,  I  maintain  that  every  substance  involves  in  its 
present  state  all  its  past  and  future  states  and  even 
expresses  the  whole  universe  according  to  its  point 
of  view,  since  nothing  is  so  far  from  anything  else 
that  there  is  no  relation  between  them.  This 
expression  would  be  particularly  complete,  however, 
with  regard  to  the  relations  to  the  parts  of  its  own 
body,  which  it  expresses  more  immediately.  Conse- 
quently, nothing  happens  to  the  substance  except 
out  of  its  own  being  and  in  virtue  of  its  own  laws, 
provided  that  we  add  the  concurrence  of  God.  It 
perceives  other  things  because  it  expresses  them 
naturally,  having  from  the  start  been  created  in  such 
a  way  that  it  can  do  this  in  a  series  of  events,  accom- 
modating itself  as  called  for,  and  it  is  in  this  agree- 
ment imposed  from  the  beginning  that  consists  what 
is  called  the  action  of  one  substance  upon  another. 
With  regard  to  corporeal  substances,  I  hold  that 
mass,  when  we  mean  by  this  what  is  divisible,  is  a 
pure  phenomenon;  that  every  substance  has  a  true 
unity  in  the  strictness  of  metaphysics;  that  it  is 
indivisible,  ingenerable,  and  incorruptible;  that  all 
matter  must  be  full  of  animated  or,  at  least,  living 
substances;  that  generation  and  corruption  are  only 
transformations  from  the  little  to  the  great,  and  vice 
versa;  that  there  is  no  particle  of  matter  in  which  is 
not  found  a  world  with  an  infinity  of  creatures 
organized  as  well  as  brought  together;  and,  above 
all,  that  the  works  of  God  are  infinitely  greater, 
more  beautiful,  and  better  ordered  than  is  commonly 
thought,  and  that  mechanism,  or  organization,  that 
is  to  say,  order,  is  essential  to  them  even  in  their 
smallest  parts.  Therefore,  no  hypothesis  can  enable 


234  CORRESPONDENCE. 

us  better  to  recognize  the  wisdom  of  God  than  mine: 
according  to  which  there  are  everywhere  substances 
indicating  God's  perfection,  and  there  are  just  so 
many  differing  reflections  of  the  beauty  of  the  uni- 
verse, where  nothing  remains  empty,  sterile,  unculti- 
vated and  without  perception.  It  must  also  be  held  as 
indubitable  that  the  laws  of  motion  and  the  changes 
of  bodies  serve  the  laws  of  justice  and  of  control, 
which  are  without  doubt  observed  the  best  way  pos- 
sible in  the  government  of  spirits;  that  is  to  say,  of 
the  intelligent  souls  which  enter  into  social  relations 
with  God  and,  together  with  him,  constitute  a  kind 
of  perfect  city  of  which  he  is  the  monarch. 

I  think  now,  M.,  that  I  have  omitted  none  of  all 
the  difficulties  which  you  spoke  of,  or  at  least  indi- 
cated, and  also  of  those  which  I  have  thought  you 
might  still  have.  It  is  true  that  this  has  increased 
the  size  of  this  letter  but  it  would  have  been  more 
difficult  to  put  my  meaning  in  less  words,  and  had 
I  attempted  it,  obscurity  might  have  been  involved. 
I  think  that  you  will  now  find  my  positions  as  well 
articulated  among  themselves  as  with  the  accepted 
opinions.  I  do  not  at  all  overthrow  established 
opinions,  but  I  explain  them  and  I  carry  them  out 
further.  If  you  might  have  the  leisure  some  day  to 
look  over  again  what  we  finally  established  regard- 
ing the  concept  of  an  individual  substance,  you  will 
perhaps  find,  that  in  granting  me  this  premise  it 
will  be  necessary  to  grant  all  the  rest.  I  have 
attempted,  however,  to  write  this  letter  in  such  a 
way  that  it  shall  explain  and  defend  itself.  It  is 
quite  possible,  indeed,  to  separate  the  questions. 
Those  who  are  unwilling  to  recognize  souls  in  ani- 
mals and  substantial  forms  elsewhere,  may,  neverthe- 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          235 

less,  approve  of  the  way  in  which  I  have  explained 
the  union  of  the  mind  and  the  body,  and  all  that  I 
have  said  regarding  true  substance.  It  will  be  for 
them  to  save  as  they  can,  without  such  forms  and 
without  a  true  unity,  whether  by  points  or  by  atoms, 
as  seems  best  to  them,  the  reality  of  matter  and  of 
corporeal  substances,  or  else  to  leave  this  undecided; 
since  investigation  can  be  cut  off  wherever  one 
thinks  best.  We  must  not,  however,  stop  half  way 
when  we  desire  to  have  true  ideas  of  the  universe 
and  of  the  perfection  of  God's  works,  which  are  able 
to  furnish  us  most  weighty  arguments  with  respect 
to  God  and  with  respect  to  our  souls. 

It  is  very  remarkable  how  Catelan  has  so  entirely 
missed  my  meaning,  as  you  suspected  he  had;  he 
advances  three  propositions  and  says  that  I  find  con- 
tradictions in  them,  while,  in  fact,  I  find  none  there, 
and  employ  these  very  propositions  to  prove  the 
absurdity  of  the  Cartesian  principle.  This  is  the 
result  of  dealing  with  men  who  take  up  things  only 
superficially.  If  it  can  happen  in  a  question  of 
mathematics  what  should  we  not  expect  in  meta- 
physics and  in  ethics.  It  is  for  this  reason  that  I 
consider  myself  fortunate  in  having  found  in  you  a 
critic  as  exact  as  he  is  fair.  I  wish  you  long  life,  as 
well  for  the  interests  of  the  public  as  for  my  own. 
I  am,  etc. 

Part  of  a  letter  sent  at  the  same  time  to  Arnauld. 

Here  is  the  reply  to  your  last  objection,  it  has 
become  a  little  long  because  I  wish  to  explain 
myself  explicitly  and  to  leave  none  of  your  doubts 
untouched.  Several  times  I  inserted  your  own 
words  which  contributed  toward  increasing  its  size. 


236  CORRESPONDENCE. 

As  I  took  all  those  positions  a  long  time  ago  and 
have  foreseen,  if  I  might  dare  to  say,  most  of  the 
objections,  they  cost  me  hardly  any  meditation,  and 
all  I  needed  to  do  was  to  pour  out  my  thoughts 
upon  paper  and  to  re-read  them  afterwards.  I  say 
this,  M.,  so  that  you  may  not  think  me  too  deeply 
engrossed  in  such  matters  at  the  expense  of  other 
necessary  business;  you  drew  me  on  to  go  so  far, 
when  you  made  objections  and  questions  which  I 
wished  to  satisfy,  as  much  in  order  to  profit  by  your 
enlightenment  as  to  make  you  recognize  my  wish  to 
disguise  nothing. 

At  the  present  time  I  am  very  busy  with  a  history 
of  the  noble  house  of  Brunswick.  I  have  looked 
over  several  archives  this  summer  and  I  am  to  make 
a  journey  in  Southern  Germany  to  seek  certain  docu- 
ments; this  does  not  prevent  my  desiring  to  learn 
your  opinion  regarding  my  explanations  when 
your  leisure  will  permit  it  and  also  regarding 
my  reply  to  Catelan  which  I  send  herewith;  I  do 
this  because  it  is  short  and,  in  my  opinion,  demon- 
strative, provided  that  it  is  read  with  the  least 
attention.  If  Catelan  does  not  do  better  than 
hitherto,  I  cannot  expect  any  enlightenment  from 
him  on  this  subject.  I  wish  you  might  be  able  to 
give  a  moment  of  serious  attention  to  it,  and  you 
would,  perhaps,  be  surprised  to  see  that  something 
which  is  so  easy  to  overthrow  has  been  accepted  as 
an  incontrovertible  principle  because  it  is  clear  that 
the  velocities  which  bodies  acquire  in  descending 
are  as  the  square  roots  of  the  heights  from  which 
they  have  fallen:  now,  if  we  leave  out  of  question 
external  resistances  a  body  can  return  exactly  to  the 
height  from  which  it  has  descended,  therefore 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          237 

Another  draft  of  the  above. 

1  herewith  send  you  my  reply  to  Catelan  which 
will,  perhaps,  be  inserted  in  The  News  of  the 
Republic  of  Letters;  we  are  at  the  beginning  again, 
and  I  made  a  mistake  in  replying  to  his  first  answer. 
I  should  simply  have  said  that  he  did  not  touch  my 
objection,  and  should  have  indicated  these  points  to 
which  a  reply  was  necessary,  as  I  have  now  done — 
I  have  added  in  my  reply  a  mechanical  problem, 
which  can  be  solved  by  geometry,  but  a  good  deal  of 
skill  must  be  used  and  I  will  see  if  M.  Catelan  will 
dare  tackle  it.  It  seems  to  me  that  he  is  not  very 
able,  and  I  am  surprised  to  see  that  among  so  many 
Cartesians  there  are  so  few  who  imitate  Descartes  in 
trying  to  advance  further. 


XXIV 

Leibniz  to  Count  Ernst  von  Hessen-Rheinfels. 

I  beg  your  Highness  to  ask  M  Arnauld  as  well  as 
yourself  if  there  is  really  so  great  an  evil  in  saying 
that  everything  (whether  a  species  or  whether  an 
individual  or  person),  has  a  certain  perfect  concept 
which  involves  all  that  can  be  truly  said  regarding 
it,  and,  according  to  this  concept,  God,  who  con- 
ceives of  everything  perfectly,  conceives  of  the  said 
thing?  And  to  ask  further  if  M.  A.  thinks  in 
good  faith  that  a  man  who  holds  such  a  position 
could  not  be  accepted  into  the  Catholic  church,  even 
when  he  sincerely  rejects  the  supposed  fatalistic 
consequence;  and  Your  Highness  may  ask  how  that 
agrees  with  what  M.  A.  formerly  wrote,  namely, 
that  no  trouble  was  made  for  a  man  in  the  Church  on 


238  CORRESPONDENCE. 

account  of  these  kinds  of  opinions,  and  if  it  is  not  to 
repulse  men  by  a  useless  and  untimely  strictness,  to 
condemn  so  easily  all  kinds  of  opinions  which  have 
nothing  to  do  with  the  faith? 

Can  it  be  denied  that  everything,  whether  genus, 
species  or  individual  has  a  complete  concept  accord- 
ing to  which  God  conceives  of  it  (he  who  conceives 
of  everything  perfectly),  a  concept  which  involves 
or  embraces  all  that  can  be  said  of  the  thing?  And 
can  it  be  denied  that  God  is  able  to  have  such  an 
individual  conception  of  Adam  or  of  Alexander  that 
it  shall  embrace  all  the  attributes,  affections,  acci- 
dents and,  in  general,  all  the  predicates  of  this  sub- 
ject? And  finally  since  St.  Thomas  could  maintain 
that  every  separate  intelligence  differed  in  kind 
from  every  other,  what  evil  will  there  be  in  saying 
the  same  of  every  person  and  in  conceiving  indi- 
viduals as  final  species,  provided  that  the  species 
shall  not  be  understood  physically  but  metaphys- 
ically or  mathematically;  for,  in  physics  when  a 
thing  engenders  something  similar  to  it,  they  are 
said  to  be  of  the  same  kind,  but  in  metaphysics  or 
in  geometry  we  say  that  things  differ  in  kind  when 
they  have  any  difference  in  the  concept  which 
suffices  to  describe  them,  so  that  two  ellipses  in 
one  of  which  the  major  and  minor  axes  are  in  the 
ratio  of  two  to  one  and  in  the  other  in  the  ratio  of 
three  to  one,  differ  in  kind.  Two  ellipses  which 
differ  only  in  magnitude  or  proportionately,  and 
where,  in  their  description,  there  is  no  difference 
of  ratio  in  the  axes,  have  no  specific  difference  or 
difference  in  kind,  for  it  must  be  remembered  that 
complete  beings  cannot  differ  merely  because  of 
differences  in  size. 


LEIBNIZ.        ARNAULIX        HESSEN-RHEINFELS.  239 

XXV 
Leibniz  to  Arnauld. 

January  14,  1688. 
Monsieur: 

Perhaps  you  will  have  seen  in  The  News  of  the 
Republic  of  Letters  for  the  month  of  September 
what  I  replied  to  M.  1'Abbe  C.  It  is  a  remarkable 
thing  to  see  how  many  people  reply,  not  to  what 
has  been  said,  but  to  what  they  have  imagined. 
This  is  what  M.  1'Abbe  has  done  up  to  the  pres- 
ent. For  this  reason  it  was  necessary  to  break  off 
abruptly,  and  bring  him  back  to  the  first  objection. 
I  have  only  taken  the  opportunity  of  this  argumen- 
tation to  put  forward  a  very  curious  geometrico- 
mechanical  problem  which  I  have  just  solved.  It 
is  to  find  what  I  call  an  isochronous  curve,  in  which 
a  body  shall  descend  uniformly  and  approach  equal 
distances  to  the  horizon  in  equal  times,  notwith- 
standing the  acceleration  it  undergoes.  This  latter 
I  offset  by  continually  changing  the  inclination.  I 
did  this  in  order  to  bring  out  something  useful  and  to 
show  M.  1'Abbe  that  the  ordinary  analysis  of  the 
Cartesians  is  too  limited  for  difficult  problems.  I 
succeeded  partly  in  this,  for  M.  Hugens*  gave  a  solu- 
tion of  the  problem  in  the  News  for  October.  I 
knew  well  enough  that  M.  Hugens  could  do  it,  and 
therefore  I  didn't  expect  that  he  would  take  the 
trouble,  or,  at  least,  that  he  would  publish  his  solu- 
tion and  set  M.  1'Abbe  free:  since,  however,  M. 
Hugens'  solution  is  in  part  enigmatical,  apparently 
to  see  if  I  can  do  it  also,  I  have  sent  him  the 
rest  of  it.  Now  we  will  see  what  M.  1  Abbe  will 

*  So  spelled  by  Leibniz.—  EdL 


240  CORRESPONDENCE. 

say  about  it. '  It  is  true  that  if  the  nature  of  the  line 
which  M.  Hugens  has  published  is  known,  the  rest  can 
be  obtained  by  ordinary  analysis,  but  without  that 
the  thing  is  difficult,  for  the  converse  of  the  rule  of 
tangents,  to  find  the  line,  having  given  the  property 
of  the  tangents,  to  which  this  proposed  problem 
reduces  itself,  is  a  problem  which  M.  Descartes  him- 
self has  confessed  in  one  of  his  letters  not  to  have 
mastered.  For,  usually,  what  I  call  transcendentals 
result,  which  have  no  degree;  and  when  the  problem 
reduces  itself  to  curves  of  a  certain  degree,  as  it 
happens  in  this  case,  an  ordinary  analyst  will  have 
difficulty  in  recognizing  it. 

I  wish,  with  all  my  heart,  that  you  might  have 
leisure  to  think  over  for  half  an  hour  my  objection 
to  the  Cartesians,  which  M.  1'Abbe  tries  to  meet. 
Your  enlightenment  and  your  sincerity  assure  me 
that  we  should  come  to  the  point  and  that  you 
would  recognize  in  good  faith  what  was  the  real  dis- 
cussion. The  discussion  is  not  long,  and  the  matter 
is  of  importance,  not  only  for  mechanics,  but  also  in 
the  realm  of  metaphysics,  because  movement  in 
itself  separated  from  force  is  something  merely 
relative  and  its  subject  cannot  be  determined;  force, 
however,  being  something  real  and  absolute,  and  its 
calculations,  as  I  clearly  show,  different  from  that  of 
motion,  we  must  not  be  surprised  if  nature  preserves 
the  same  quantity  of  force  but  not  the  same  quantity 
of  motion.  It  follows  that  there  is  in  nature  some- 
thing besides  extension  and  motion,  unless  ajl 
force  or  energy  be  denied  to  things,  which  would 
be  to  change  them  from  substances  into  modes,  as 
Spinoza  does,  who  holgls  that  God  alone  is  a  sub- 
stance and  that  all  qther  things  are  modifications  of 


LEIBNIZ.       ARNAULD.       HESSEN-RHEINFELS.          241 

him.  Spinoza  is  full  of  confused  reveries  and  his 
pretended  demonstrations  de  Deo  have  only  an 
apparent  truth.  However,  I  hold  that  one  created 
substance,  in  metaphysical  strictness,  does  not  act 
upon  another,  that  is  to  say,  with  a  real  influence; 
furthermore,  it  is  impossible  to  explain  distinctly 
in  what  this  influence  consists  unless  we  refer  it  to 
God,  whose  operation  is  a  continual  creation,  and 
the  source  of  this  influence  is  the  essential  depend- 
ence of  created  things.  If  we  wish  to  speak  as 
ordinary  men  do,  who  say  that  one  substance  acts 
upon  another,  we  must  give  some  other  conception 
to  what  is  called  action.  It  would  take  too  long  to 
develop  this  point  and  I  refer  to  my  last  letter,  which 
is  prolix  enough. 

I  do  not  know  whether  the  Rev.  Father  Male- 
branche  has  replied  to  my  answer  given  in  one  of 
the  summer  months  of  last  year,  where  I  advanced 
another  general  principle  useful  in  mechanics  as  in 
geometry,  which  clearly  overthrew  all  the  laws  of 
motion  that  Descartes  put  forward  as  well  as  those 
of  Malebranche  himself,  together  with  what  he  said 
in  The  News  to  defend  them. 

Some  day,  if  I  find  leisure  I  hope  to  write  out  my 
meditations  upon  the  general  characteristic  or 
method  of  universal  calculus,  which  should  be  of 
service  in  the  other  sciences  as  well  as  in  mathe- 
matics. I  have  already  made  some  successful 
attempts.  I  have  definitions,  axioms,  and  very 
remarkable  theorems  and  problems  in  regard  to 
coincidence,  determination  (or  de  unico),  similitude, 
relation  in  general,  power  or  cause,  and  substance, 
and  everywhere  I  advance  with  symbols  in  a  precise 
and  strict  manner  as  in  algebra.  I  have  made  some 


242  CORRESPONDENCE. 

applications  of  it  in  jurisprudence,  and  it  can  be 
truly  said  that  there  are  no  authors  whose  style 
approaches  nearer  that  of  the  geometers  than  the 
style  of  the  jurists  in  the  Digests.  But  you  will  ask 
how  is  calculation  to  be  applied  to  conjectural  mat- 
ters. I  reply  that  it  is  in  the  way  that  Pascal, 
Hugens,  and  others,  have  given  demonstrations  of 
possible  chances,  Because  the  most  probable  and 
the  most  certain  can  always  be  determined  in  so  far 
as  it  is  possible  to  know  anything  ex  datis. 

I  do  not  however  wish  to  take  more  of  your  time, 
and  perhaps  I  have  already  taken  too  much.  I 
should  not  dare  to  do  it  so  frequently,  if  the  matters 
upon  which  I  desire  to  have  your  criticisms  were  not 
important.  I  pray  God  to  prolong  your  life  a  long 
time,  so  that  we  may  always  profit  by  your  enlighten- 
ment. I  am,  with  zeal,  etc. 

XXVI 
Leibniz  to  Arnauld. 

Venice,  March  23,  1690. 

I  am  now  on  the  point  of  returning  home  after  a 
long  journey,  undertaken  under  the  orders  of  my 
Prince  for  the  purpose  of  historical  investigations. 
And  I  have  found  diplomas,  certificates  and  indubi- 
table proofs  sufficient  to  establish  the  common  origin 
of  the  noble  Houses  of  Brunswick  and  Este,  which 
Justel,  du  Cange  and  others  had  strong  grounds  for 
calling  in  question,  because  there  were  contradic- 
tions and  errors  on  the  part  of  the  historians  of  Este 
in  this  respect,  together  with  a  complete  confusion 
in  dates  and  personages. 

At  present  I  am  thinking  of  returning  to  my  old 


LEIBNIZ.       ARNAULD.       HESSKN-RHEINFELS.          243 

life  and  of  taking  up  my  former  occupations  again. 
I  wrote  to  you  two  years  ago,  a  little  before  my 
departure,  and  I  take  the  same  liberty  again,  for  the 
purpose  of  asking  after  your  health  and  to  let  you 
know  how  constantly  the  thought  of  your  well- 
known  merits  are  in  my  mind.  When  I  was  at 
Rome,  I  saw  the  denunciation  of  a  new  letter  which 
is  attributed  to  you  or  to  your  friends.  Since  then 
I  have  seen  a  letter  of  the  Rev.  Father  Mabillon's  to 
one  of  my  friends  in  which  he  says  that  the  Rev. 
Father  Tellier's  apology  for  the  missionaries  against 
the  practical  morality  of  the  Jesuits  had  given  to 
many  persons  favorable  impressions  of  these  Fathers, 
but  he  had  heard  that  you  had  replied  to  it,  and  that 
it  was  said  you  had  with  geometrical  logic  com- 
pletely overthrown  the  reasoning  of  this  Father. 
All  this  has  led  me  to  think  that  you  are  still  in  a 
condition  to  render  service  to  the  public,  and  I  pray 
God  that  it  may  be  so  for  a  long  time  yet.  It  is 
true  that  I  have  a  personal  interest  in  this,  but  it  is  a 
praiseworthy  interest  since  I  am  given  a  means  of 
being  instructed,  whether  in  common  with  all  the 
others,  who  will  read  your  works,  or  in  particular 
when  your  criticisms  shall  instruct  me,  provided  the 
little  leisure  which  you  have  may  still  permit  me  to 
hope  for  this  advantage  at  times. 

As  this  journey  has  served  in  part  to  release  my 
mind  from  routine  business,  I  have  had  the  satisfac- 
tion of  conversing  with  several  able  men  on  matters 
of  learning  and  science,  and  I  have  communicated 
to  some  of  them  my  own  views,  which  you  are 
acquainted  with,  in  order  to  profit  by  the  doubts  and 
difficulties  which  they  raised,  and  there  were  some 
of  these  men  who,  not  satisfied  with  the  current 


244  CORRESPONDENCE. 

doctrines,  found  an  unusual  satisfaction  in  certain 
of  my  positions.  This  has  led  me  to  put  them  down 
in  writing  so  that  they  may  be  communicated  more 
easily,  and  some  day,  perhaps,  1  will  have  a  few 
copies  printed  without  my  name,  merely  to  circulate 
them  among  my  friends  in  order  to  obtain  their 
criticisms.  I  should  like  you  to  be  able  to  examine 
them  first  and  therefore  I  have  made  the  following 
abstract: 

A  body  is  an  aggregation  of  substances,  and  is 
not  a  substance,  properly  speaking.  Consequently, 
in  all  bodies  must  be  found  indivisible  substances 
which  cannot  be  generated  and  are  not  corruptible, 
having  something  which  corresponds  to  souls. 

All  these  substances  have  been  always  and  will 
always  be  united  to  organic  bodies  diversely  trans- 
formable. 

Each  of  these  substances  contains  in  its  nature  the 
law  of  the  continuous  progression  of  its  own  work- 
ings and  all  that  has  happened  to  it  and  all  that  will 
happen  to  it. 

Excepting  the  dependence  upon  God,  all  these 
activities  come  from  its  own  nature. 

Each  substance  expresses  the  whole  universe, 
some  substances,  however,  more  distinctly  than 
others,  each  one  especially  distinctly  with  regard 
to  certain  things  and  according  to  its  own  point  of 
view. 

The  union  of  the  soul  with  the  body  and  even  the 
action  of  one  substance  upon  another  consists  only 
in  the  perfect  mutual  accord,  expressly  established 
by  the  ordinance  of  the  first  creation,  by  virtue  of 
which  each  substance  following  its  own  laws  falls  in 
with  what  the  others  require,  and  thus  the  activities 


LEIBNIZ.       ARNAULD.       HKSSEN-RHEINFELS.          245 

of  the  one  follow  or  accompany  the  activities  or 
changes  of  the  other. 

Intellects,  or  souls  which  are  capable  of  reflection 
and  of  knowing  the  eternal  truths  and  God,  have 
many  privileges  that  exempt  them  from  the  trans- 
formations of  bodies. 

In  regard  to  them  moral  laws  must  be  added  to 
physical  laws. 

It  is  for  them  principally  that  every  thing  has  been 
made. 

They,  taken  together,  constitute  the  Republic  of 
the  Universe,  with  God  as  the  monarch. 

There  is  perfect  justice  and  order  observed  in 
this  city  of  God,  and  there  is  no  evil  action  without 
its  chastisement,  nor  any  good  action  without  its 
proportionate  reward. 

The  better  things  are  understood,  the  more 
are  they  found  beautiful  and  conformable  to  the 
desires  which  a  wise  man  might  form. 

We  must  always  be  content  with  the  ordering  of 
the  past  because  it  has  absolutely  conformed  to  the 
will  of  God,  which  can  be  known  by  the  events,  but 
we  must  try  to  make  the  future,  in  so  far  as  it 
depends  upon  us,  conform  to  the  presumptive  will 
of  God  or  to  his  commandments,  to  beautify  our 
Sparta  and  to  labor  in  well-doing,  without,  however, 
being  cast  down  when  unsuccessful,  in  the  firm 
belief  that  God  will  know  how  to  find  the  most  fit- 
ting times  for  changes  to  the  better. 

Those  who  are  not  content  with  the  ordering  of 
things  cannot  boast  of  loving  God  properly. 

Justice  is  nothing  else  than  love  felt  by  the 
wise. 

Charity  is  universal  benevolence  whose  fulfillment 


246  CORRESPONDENCE. 

the  wise  carry  out  conformably  to  the  dictates  of 
reason  so  as  to  obtain  the  greatest  good. 

Wisdom  is  the  science  of  happiness  or  of  the 
means  of  attaining  the  lasting  contentment  which 
consists  in  the  continual  achievement  of  a  greater 
perfection  or  at  least  in  variations  of  the  same  degree 
of  perfection. 

In  regard  to  the  subject  of  physics:  the  nature  of 
force  must  be  understood  as  wholly  different  from 
motion,  which  is  something  more  relative.  Force 
must  be  measured  by  the  quantity  of  effect:  there  is 
an  absolute  force,  a  directive  force  and  a  respective 
force. 

Each  of  these  forces  is  conserved  in  the  same 
quantity  in  the  universe,  or  in  each  machine  which 
has  no  communication  with  others,  and  the  two  lat- 
ter forces  taken  together  compose  the  former  or  the 
absolute  force.  The  same  amount  of  motion,  how- 
ever, is  not  conserved,  for  I  can  show  that  if  it  were, 
perpetual  motion  would  be  possible,  and  that  an 
effect  would  be  greater  than  its  cause. 

Some  time  ago  I  published  in  the  Acts  of 
Leipsic  an  essay  in  the  domain  of  physics  for  the 
purpose  of  finding  the  physical  causes  of  the  astral 
motions.  I  assume  as  basal  that  every  motion  of  a 
solid  in  a  fluid,  where  the  motion  is  in  a  curved  line 
or  the  velocity  is  constantly  changing,  is  derived  from 
the  motion  of  the  fluid  itself.  Whence  I  draw  the 
conclusion  that  the  heavenly  bodies  have  deferent 
but  fluid  orbs,  which  we  may  call  with  Descartes 
and  with  the  ancients,  vortexes.  I  think  there  are 
neither  vacuums  nor  atoms,  for  these  are  things  far 
removed  from  the  perfection  of  God's  works,  and 
that  every  motion  is  propagated  from  one  body  to 


LEIBNIZ.        ARNAULD.        HESSEN-RHEINFELS.          247 

all  other  bodies,  although  more  feebly  as  the  dis- 
tances are  greater.  Supposing  that  all  the  great 
globes  in  the  universe  have  something  analogous  to 
magneti?m,  I  think  that  in  addition  to  a  certain  tend- 
ency which  causes  them  to  maintain  the  parallel- 
ism of  their  axes,  they  have  a  kind  of  attraction 
whence  arises  something  comparable  to  gravity. 
We  can  picture  this  by  imagining  rays  of  some 
material  substance  which  is  trying  to  move  away 
from  a  center  and  consequently  pushes  others  which 
have  not  this  tendency  toward  the  center.  We  may 
compare  these  rays  of  attraction  with  those  of  light, 
and  by  the  same  law  which  holds  in  illumination  we 
shall  find  that  the  attraction  is  inversely  as  the 
square  of  the  distance. 

These  things  agree  wonderfully  with  the  phe- 
nomena. Kepler  found  that  in  general  the  areas  of 
the  orbits  of  the  planets  described  by  radii  drawn 
from  the  sun  to  the  orbits  are  in  proportion  to  the 
times  of  the  revolutions  around  the  sun,  and  I  have 
demonstrated  an  important  general  proposition, 
namely,  that  all  those  bodies  which  revolve  in 
harmonic  motion  (that  is  to  say,  so  move  that  their 
distances  from  the  center  are  in  arithmetical  pro- 
gression, while  their  velocities  are  in  harmonic 
progression  or  inversely  as  the  distances),  and 
moreover,  if  these  bodies  have  a  paracentric 
motion  (that  is  to  say,  are  heavy  or  light  as 
regards  the  same  center,  whatever  law  this  attrac- 
tion or  repulsion  may  obey) — all  such  bodies 
describe  areas  which  vary  necessarily  as  the  times, 
just  as  Kepler  observed  in  the  case  of  the 
planets.  I  conclude  that  the  deferent  fluid  orbs 
of  the  planets  revolve  harmonically,  and  I  give  an  a 


248  CORRESPONDENCE. 

priori  reason  for  this.  Now,  empirically  observing 
that  in  fact  this  motion  is  elliptical,  I  find  that  the 
law  of  paracentric  motions,  which  when  combined 
with  the  harmonic  revolutions  describe  ellipses, 
ought  to  be  such  that  the  attraction  is  inversely 
as  the  squares  of  the  distances,  that  is,  exactly  the 
same  as  what  we  found  above  to  be  true  a  priori  by 
the  laws  of  radiation.  From  this  I  then  deduce 
special  characteristics  and  the  whole  was  broached 
in  my  publication  in  the  Acts  of  Leipsic  some  time 
ago. 

I  will  say  nothing  of  my  calculus  of  increments  or 
differences,  by  which  I  determine  the  tangents  with- 
out eliminating  irrationals  and  fractions  even  when 
unknown  quantities  are  involved  in  them  and  by 
which  I  subject  quadratics  and  transcendental  prob- 
lems to  analysis.  Neither  will  I  speak  of  an  entirely 
new  analysis  confined  to  Geometry  and  differing 
entirely  from  Algebra,  and  even  less  of  certain  other 
subjects  which  I  have  not  yet  had  the  time  to 
develop.  I  should  have  liked  to  be  able  to  explain 
them  all  to  you  in  a  few  words,  so  as  to  have  upon 
them  your  opinion,  which  would  be  of  infinite  serv- 
ice to  me,  had  you  as  much  leisure  as  I  have  defer- 
ence for  your  criticism.  Your  time,  however,  is  too 
precious,  and  my  letter  is  already  quite  long. 
Therefore  I  bring  it  to  an  end  here,  and  am 
sincerely,  etc. 


THE   MONADOLOGY. 


THE  MONADOLOGY. 

1.  The    Monad,  of  which  we  will  speak  here,  is 
nothing  else  than  a  simple  substance,  which  goes  to 
make  up  composites;   by  simple,  we  mean  without 
parts. 

2.  There  must  be  simple  substances  because  there 
are  composites;  for  a  composite  is  nothing  else  than 
a  collection  or  aggregatum  of  simple  substances. 

3.  Now,    where   there   are    no   constituent    parts 
there  is  possible  neither  extension,   nor  form,  nor 
divisibility.     These  Monads  are  the  true  Atoms  of 
nature,  and,  in  fact,  the  Elements  of  things. 

4.  Their  dissolution,  therefore,  is  not  to  be  feared 
and  there  is  no  way  conceivable  by  which  a  simple 
substance  can  perish  through  natural  means. 

5.  For  the  same  reason  there  is  no  way  conceiv- 
able by  which  a  simple  substance  might,   through 
natural   means,    come  into   existence,   since  it  can 
not  be  formed  by  composition. 

6.  We  may  say  then,  that  the  existence  of  Monads 
can  begin  or  end  only  all  at  once,  that  is  to  say,  the 
Monad   can  begin  only  through   creation  and  end 
only  through    annihilation.     Composites,   however, 
begin  or  end  gradually 

7.  There    is   also    no   way   of   explaining   how  a 
Monad  can  be  altered  or  changed  in  its  inner  being 
by  any  other  created  thing,  since  there  is  no  possi- 
bility of  transposition  within  it,  nor  can  we  conceive 

251 


252  LEIBNIZ. 

of  any  internal  movement  which  can  be  produced, 
directed,  increased  or  diminished  there  within  the 
substance,  such  as  can  take  place  in  the  case  of 
composites  where  a  change  can  occur  among  the 
parts.  The  Monads  have  no  windows  through 
which  anything  may  come  in  or  go  out.  The 
Attributes  are  not  liable  to  detach  themselves  and 
make  an  excursion  outside  the  substance,  as  could 
sensible  species  of  the  Schoolmen.  In  the  same 
way  neither  substance  nor  attribute  can  enter  from 
without  into  a  Monad. 

8.  Still  Monads  must  needs  have  some  qualities, 
otherwise  they  would  not  even  be  existences.     And 
if  simple  substances  did  not  differ  at  all  in  their 
'qualities,  there  would  be  no  means  of  perceiving 
any  change  in  things.     Whatever  is  in  a  composite 
can  come   into  it  only  through  its  simple  elements 
and  the  Monads,  if  they  were  without  qualities,  since 
they  do    not   differ   at    all    in   quantity,   would   be 
indistinguishable  one  from  another.     For  instance, 
if  we  imagine  a  plenum  or  completely  filled  space, 
where  each  part  receives  only  the  equivalent  of  its 
own  previous  motion,  one  state  of  things  would  not 
be  distinguishable  from  another. 

9.  Each  Monad,  indeed,  must  be  different  from 
every  other.      For  there  are  never  in   nature  two 
beings  which  are  exactly  alike,  and  in  which  it  is 
not  possible  to  find  a  difference  either  internal  or 
based  on  an  intrinsic  property. 

10.  I   assume   it  as  admitted  that  every  created 
being,  and  consequently  the  created  Monad,  is  sub- 
ject to  change,   and  indeed  that  this  change  is  con- 
tinuous in  each. 

11.  It  follows  from  what  has  just  been  said,  that 


MONADOLOGY.  253 

the  natural  changes  of  the  Monad  come  from  an 
internal  principle,  because  an  external  cause  can 
have  no  influence  upon  its  inner  being. 

12.  Now  besides  this  principle  of  change  there 
must  also  be  in  the  Monad  a  manifoldness  which 
changes.       This    manifoldness    constitutes,    so    to 
speak,   the  specific  nature  and  the  variety  of  the 
simple  substances. 

13.  This  manifoldness  must  involve  a  multiplicity 
in  the  unity  or  in  that  which  is  simple.     For  since 
every  natural  change  takes  place  by  degrees,  there 
must  be  something  which  changes  and  something 
which  remains  unchanged,  and  consequently  there 
must  be  in  the  simple  substance  a  plurality  of  con- 
ditions and  relations,  even  though  it  has  no  parts. 

14.  The    passing    condition    which   involves  and 
represents  a    multiplicity  in  the  unity,   or  in  the 
simple  substance,  is  nothing  else  than  what  is  called 
Perception.     This  should  be  carefully  distinguished 
from  Apperception  or  Consciousness,  as  will  appear 
in  what  follows.     In  this  matter  the  Cartesians  have 
fallen  into  a  serious  error,  in  that  they  treat  as  non- 
existent those  perceptions  of  which  we  are  not  con- 
scious.    It  is  this  also  which  has  led  them  to  believe 
that  spirits  alone  are  Monads  and  that  there  are  no 
souls  of  animals  or  other  Entelechies,  and  it  has  led 
them  to  make  the   common   confusion   between  a 
protracted    period    of   unconsciousness  and   actual 
death.      They    have    thus   adopted   the    Scholastic 
error  that  souls  can  exist  entirely  separated  from 
bodies,  and  have  even  confirmed  ill-balanced  minds 
in  the  belief  that  souls  are  mortal. 

15.  The    action    of  the   internal   principle  which 
brings  about  the  change  or  the  passing  from  one 


254  LEIBNIZ. 

perception  to  another  may  be  called  Appetition. 
It  is  true  that  the  desire  (I'appetit)  is  not  always 
able  to  attain  to  the  whole  of  the  perception  which 
it  strives  for,  but  it  always  attains  a  portion  of  it 
and  reaches  new  perceptions. 

16.  We,  ourselves,  experience  a  multiplicity  in  a 
simple  substance,  when  we  find  that  the  most  trifling 
thought  of  which  we  are  conscious  involves  a  variety 
in  the  object.     Therefore  all  those  who  acknowl- 
edge that  the  soul  is  a  simple  substance  ought  to 
grant  this  multiplicity  in  the  Monad,  and  Monsieur 
Bayle  should  have  found  no  difficulty  in  it,  as  he  has 
done  in  his  Dictionary,  article  "Rorarius." 

17.  It  must  be  confessed,  however,  that  Percep- 
tion, and    that  which   depends   upon    it,    are   inex- 
plicable by  mechanical  causes,   that  is  to  say,  by 
figures  and  motions.     Supposing  that  there  were  a 
machine  whose  structure  produced  thought,  sensa- 
tion, and  perception,   we  could  conceive    of  it  as 
increased  in  size  with  the  same  proportions  until 
one  was  able  to  enter  into  its  interior,  as  he  would 
into  a  mill.     Now,  on  going  into  it  he  would  find 
only  pieces  working  upon  one  another,  but  never 
would  he  find  anything  to  explain  Perception.     It 
is  accordingly  in  the  simple  substance,  and  not  in 
the  composite  nor  in  a  machine  that  the  Perception 
is  to  be  sought.       Furthermore,    there  is    nothing 
besides  perceptions  and  their  changes  to  be  found  in 
the  simple  substance.     And  it  is  in  these  alone  that 
all  the  internal  activities  of  the  simple  substance 
can  consist. 

18.  All  simple  substances  or  created  Monads  may 
be  called  Entelechies,  because   they  have  in  them- 
selves a  certain  perfection    («x«w<ri  TO  «vr«Xes).     There 


MONADOLOGV.  255 

is  in  them  a  sufficiency  (avrop«ia)  which  makes  them 
the  source  of  their  internal  activities,  and  renders 
them,  so  to  speak,  incorporeal  Automatons. 

19.  If  we  wish  to  designate  as  soul  everything 
which  has  perceptions  and  desires  in  the  general 
sense  that    I  have  just  expJained,   all  simple  sub- 
stances or  created  Monads  could  be  called  souls. 
But  since  feeling  is  something  more  than  a  mere 
perception    I    think    that    the    general    name    of 
Monad  or  Entelechy  should  suffice  for  simple  sub- 
stances which  have  only  perception,  while  we  may 
reserve  the  term  Soul  for  those  whose  perception  is 
more  distinct  and  is  accompanied  by  memory. 

20.  We  experience  in  ourselves  a  state  where  we 
remember  nothing  and  where  we  have  no  distinct 
perception,  as  in  periods  of  fainting,  or  when  we  are 
overcome  by  a  profound,  dreamless  sleep.     In  such 
a  state  the  soul  does  not  sensibly  differ  at  all  from  a 
simple  Monad.     As  this  state,  however,  is  not  per- 
manent and  the  soul  can  recover  from  it,  the  soul  is 
something  more. 

21.  Nevertheless  it  does  not  follow  at  all  that  the 
simple  substance  is  in  such  a  state  without  percep- 
tion.    This  is  so  because  of  the  reasons  given  above; 
for  it  cannot  perish,  nor  on  the  other  hand  would  it 
exist  without  some  affection  and  the  affection   is 
nothing  else  than  its  perception.     When,  however, 
there  are  a  great  number  of  weak  perceptions  where 
nothing  stands  out  distinctively,  we  are  stunned;  as 
when  one  turns  around  and  around  in  the  same  direc- 
tion, a  dizziness  comes  on,  which  makes  him  swoon 
and  makes  him  able  to  distinguish  nothing.     Among 
animals,   death  can  occasion  this  state  for  quite  a 
period. 


256  LEIBNIZ. 

22.  Every  present  state  of  a  simple  substance  is  a 
natural  consequence  of  its  preceding  state,  in  such 
a  way  that  its  present  is  big  with  its  future. 

23.  Therefore,  since  on  awakening  after  a  period 
of  unconsciousness  we  become  conscious  of  our  per- 
ceptions, we  must,  without  having  been  conscious  of 
them,  have  had  perceptions  immediately  before;  for 
one  perception  can  come  in  a  natural  way  only  from 
another  perception,  just  as  a  motion  can  come  in  a 
natural  way  only  from  a  motion. 

24.  It  is  evident  from  this  that  if  we  were  to  have 
nothing  distinctive,  or  so  to  speak  prominent,  and 
of  a  higher  flavor  in  our  perceptions,  we  should  be 
in  a  continual  state  of  stupor.    This  is  the  condition 
of  Monads  which  are  wholly  bare. 

25.  We   see   that   nature   has    given   to    animals 
heightened  perceptions,  having  provided  them  with 
organs  which  collect  numerous  rays  of  light  or  numer- 
ous waves  of  air  and  thus  make  them  more  effective  in 
their  combination.     Something  similar  to  this  takes 
place  in  the  case  of  smell,  in  that  of  taste  and  of 
touch,  and  perhaps  in  many  other  senses  which  are 
unknown  to  us.     I  shall  have  occasion  very  soon  to 
explain  how  that  which  occurs  in  the  soul  represents 
that  which  goes  on  in  the  sense-organs. 

26.  The  memory  furnishes  a  sort  of  consecutive- 
ness  which  imitates  reason  but  is  to  be  distinguished 
from  it.     We  see  that  animals  when  they  have  the 
perception  of  something  which  they  notice  and  of 
which  they  have  had  a  similar  previous  perception, 
are  led  by  the  representation  of  their  memory  to 
expect  that  which  was  associated  in  the  preceding 
perception,  and  they  come  to  have  feelings  like  those 
which  they  had  before.     For  instance,  if  a  stick  be 


MONADOLOGY.  257 

shown  to  a  dog,  he  remembers  the  pain  which  it  has 
caused  him  and  he  whines  or  runs  away. 

27.  The  vividness  of  the  picture,  which  comes  to 
him  or  moves  him,  is  derived  either  from  the  magni- 
tude or  from  the  number  of  the  previous  perceptions. 
For,  oftentimes,  a  strong  impression  brings  about,  all 

'at  once, the  same  effect  as  a  long-continued  habit  or 
as  a  great  many  re-iterated,  moderate  perceptions. 

28.  Men  act  in  like  manner  as  animals,  in  so  far 
as  the  sequence  of  their  perceptions  is  determined 
only  by  the  law  of  memory,  resembling  the  empir- 
ical physicians     who    practice  simply,   without  any 
theory,  and  we  are  empiricists  in  three-fourths  of  our 
actions.     For  instance,  when  we  expect  that  there 
will  be  day-light  to-morrow,  we  do  so  empirically, 
because  it  has  always  happened  so  up  to  the  present 
time.      It  is  only  the  astronomer  who  uses  his  reason 
in  making  such  an  affirmation. 

29.  But  the  knowledge  of  eternal  and  necessary 
truths  is    that  which   distinguishes    us    from    mere 
animals  and  gives  us  reason  and  the  sciences,  thus 
raising  us  to  a  knowledge  of  ourselves  and  of  God. 
This  is  what  is  called  in  us  the  Rational  Soul  or  the 
Mind. 

30.  It  is  also  through  the  knowledge  of  necessary 
truths  and  through  abstractions  from  them  that  we 
come  to  perform  Reflective  Acts,  which  cause  us  to 
think  of  what  is  called  the  I,  and  to  decide  that  this 
or  that  is  within  us.     It  is  thus,  that  in  thinking 
upon  ourselves   we  think   of  being,  of  substance,  of 
the    simple  and  composite,    of  a  material  thing   and 
of  God  himself,  conceiving  that  what  is  limited  in 
us  is  in  him  without  limits.     These  Reflective  Acts 
furnish  the  principal  objects  of  our  reasonings. 


258  LEIBNIZ. 

31.  Our  reasoning  is  based  upon  two  great  prin- 
+     ciples:    first,    that  of    Contradiction,   by  means   of 

which  we  decide  that  to  be  false  which  involves 
contradiction  and  that  to  be  true  which  contradicts 
or  is  opposed  to  the  false. 

32.  And     second,     the     principle     of     Sufficient 
Reason,  in  virtue  of  which  we  believe  that  no  fact 
can  be  real  or  existing  and  no  statement  true  unless 
it  has  a  sufficient  reason  why  it  should  be  thus  and 
not   otherwise.       Most   frequently,   however,   these 
reasons  cannot  be  known  by  us. 

33.  There  are  also  two  kinds  of  Truths:  those  of 
"'  Reasoning    and    those    of    Fact.      The    Truths    of 

Reasoning  are  necessary,  and  their  opposite  is 
impossible.  Those  of  Fact,  however,  are  con- 
tingent, and  their  opposite  is  possible.  When  a 
truth  is  necessary,  the  reason  can  be  found  by 
analysis  in  resolving  it  into  simpler  ideas  and  into 
simpler  truths  until  we  reach  those  which  are  pri- 
mary. 

34.  It  te  thus  that  with  mathematicians  the  Spec- 
ulative   Theorems    and   the   practical    Canons   are 
reduced    by  analysis   to    Definitions,    Axioms,  and 
Postulates. 

35.  There  are    finally  simple   ideas  of  which  no 
definition  can  be  given.     There  are  also  the  Axioms 
and  Postulates  or,  in  a  word,  the  primary  principles 
which  cannot  be  proved  and,  indeed,  have  no  need 
of  proof.     These  are  identical  propositions  whose 
opposites  involve  express  contradictions. 

36.  But  there  must  be  also  a  sufficient  reason  for 
contingent  truths  or  truths  of  fact;    that  is  to  say, 
for    the    sequence    of     the    things    which    extend 
throughout  the  universe  of  created  beings,  where 


MONADOLOGY.  259 

the  analysis  into  more  particular  reasons  can  be 
continued  into  greater  detail  without  limit  because 
of  the  immense  variety  of  the  things  in  nature  and 
because  of  the  infinite  division  of  bodies.  There  is 
an  infinity  of  figures  and  of  movements,  present  and 
past,  which  enter  into  the  efficient  cause  of  my 
present  writing,  and  in  its  final  cause  there  are  an 
infinity  of  slight  tendencies  and  dispositions  of  my 
soul,  present  and  past. 

37.  And  as  all  this  detaiPagain  involves  other  and 
more  detailed  contingencies,  each  of  which  again 
has  need  of  a  similar  analysis  in  order  to  find  its 
explanation,     no    real    advance    has    been    made. 
Therefore,   the  sufficient  or   ultimate   reason   must 
needs  be  outside  of  the  sequence  or  series  of  these 
details  of  contingencies,  however  infinite  they  may 
be. 

38.  It  is  thus  that  the  ultimate  reason  for  things 
must  be  a  necessary  substance,  in  which  the  detail 
of  the  changes  shall  be  present  merely  potentially, 
as  in  the  fountain-head,  and  this  substance  we  call 
God. 

39.  Now,  since  this  substance  is  a  sufficient  reason 
for  all  the  above  mentioned  details,  which  are  linked 
together  throughout,  there  is  but  one  God,  and  this 
God  is  sufficient. 

40.  We   may  hold   that   the   supreme   substance, 
which  is  unique,  universal  and  necessary  with  noth- 
ing independent  outside  of  it,  which  is  further  a  pure 
sequence  of  possible  being,   must  be   incapable  of 
limitation  and  must  contain  as  much  reality  as  pos- 
sible. 

41.  Whence  it  follows  that  God  is  absolutely  per- 
fect, perfection  being  understood  as  the  magnitude 


260  LEIBNIZ. 

of  positive  reality  in  the  strict  sense,  when  the 
limitations  or  the  bounds  of  those  things  which  have 
them  are  removed.  There  where  there  are  no 
limits,  that  is  to  say,  in  God,  perfection  is  abso- 
lutely infinite. 

42.  It  follows  also  that  created  things  derive  their 
perfections  through  the  influence  of  God,  but  their 
imperfections  come  from  their  own  natures,  which 
cannot  exist  without    limits.      It    is   in    this   latter 
that  they  are  distinguished  from  God.     An  example 
of  this  original  imperfection  of  created  things  is  to 
be  found  in  the  natural  inertia  of  bodies. 

43.  It  is  true,  furthermore,  that  in  God  is  found 
not  only  the  source  of  existences,  but  also  that  of 
essences,  in  so  far  as  they  are  real.     In  other  words, 
he  is  the  source  of  whatever  there  is  real  in  the  pos- 
sible.    This  is  because  the  Understanding  of  God  is 
in  the  region  of  eternal  truths  or  of  the  ideas  upon 
which  they  depend,  and  because  without  him  there 
would  be  nothing  real  in  the  possibilities  of  things, 
and   not  only  would  nothing  be  existent,    nothing 
would  be  even  possible. 

44.  For  it  must  needs  be  that  if  there  is  a  reality 
in  essences  or  in  possibilities  or  indeed  in  the  eternal 
truths,  this  reality  is  based  upon  something  existent 
and  actual,  and,   consequently,  in  the  existence  of 
the  necessary  Being  in  whom  essence  includes  exist- 
ence or  in  whom  possibility  is  sufficient  to  produce 
actuality. 

45.  Therefore  God  alone  (or  the  Necessary  Being) 
has  this  prerogative  that  if  he  be  possible  he  must 
necessarily  exist,  and,  as  nothing  is  able  to  prevent 
the  possibility  of  that  which  involves  no  bounds,  no 
negation,  and  consequently,   no  contradiction,  this 


MONADOLOGY.  261 

alone  is  sufficient  to  establish  a  priori  his  existence. 
We  have,  therefore,  proved  his  existence  through 
the  reality  of  eternal  truths.  But  a  little  while  ago 
we  also  proved  it  a  posteriori,  because  contingent 
beings  exist,  which  can  have  their  ultimate  and 
sufficient  reason  only  in  the  necessary  being  which, 
in  turn,  has  the  reason  for  existence  in  itself. 

46.  Yet  we  must  not  think  that  the  eternal  truths 
being  dependent  upon   God  are  therefore  arbitrary 
and  depend  upon  his  will,  as  Descartes  seems  to  have 
held,  and  after  him  Monsieur  Poiret.     This  is  the 
case  only  with  contingent  truths  which  depend  upon 
fitness  or  the  choice  of  the  greatest  good;  necessary 
truths  on  the  other  hand  depend  solely  upon  his 
understanding  and  are  the  inner  objects  of  it. 

47.  God  alone  is  the  ultimate  unity  or  the  orig- 
inal simple  substance,  of  which  all  created  or  deriva- 
tive Monads  are  the  products,  and  arise,  so  to  speak, 
through  the  continual  outflashings  of  the  divinity 
from  moment  to  moment,  limited  by  the  receptivity 
of  the  creature  to  whom  limitation  is  an  essential. 

48.  In    God   are   present:    Power,    which    is    the 
source  of  everything;    Knowledge,  which  contains 
the  details  of  the  ideas;  and,   finally,  Will,  which 
produces  or  effects  changes  in  accordance  with  the 
principle  of  the  greatest  good.     To  these  correspond 
in  the  created  Monad,  the  subject  or  the  basis  of  the 
faculty  of  perception  and  the  faculty  of  appetition. 
In  God  these   attributes  are  absolutely  infinite  or 
perfect,   while    in  the    created    Monads   or    in    the 
entelechies    (perfectihabies,  as  Hermolaus   Barbarus 
translates  this  word),  they  are  imitations  approach- 
ing him  in  proportion  to  their  perfection. 

49.  A  created  thing  is  said  to  act  outwardly  in 


262  LEIBNIZ. 

so  far  as  it  has  perfection,  and  to  suffer  from  another 
in  so  far  as  it  is  imperfect.  Thus  action  is  attributed 
to  the  Monad  in  so  far  as  it  has  distinct  perceptions, 
and  passion  or  passivity  is  attributed  in  so  far  as 
it  has  confused  perceptions. 

50.  One    created    thing    is    more    perfect    than 
another  when  we  find  in  the  first  that  which  gives 
an  a  priori  reason  for  what  occurs   in  the  second 
This  is  why  we  say  that  one  acts  upon  the  other. 

51.  In  the  case  of  simple  substances,  the  influence 
which  one  Monad  has  upon  another  is  only  ideal. 
It  can  have  its  effect  only  through  the  mediation  of 
God,  in  so  far  as  in  the  Ideas  of  God  each  Monad 
can   rightly  demand    that  God,    in   regulating   the 
others   from  the  beginning  of  things,  should  have 
regarded    it  also.     For,    since  one  created   Monad 
cannot    have  a   physical    influence  upon  ( the  inner 
being  of    another,    it    is  only  through   this   primal 
regulation    that    one    can    have    dependence   upon 
another. 

52.  It  is  thus  that  among  created  things  action 
and  passion  are  reciprocal.     For  God,  in  comparing 
two  simple  substances,    finds   in  each  one  reasons 
obliging  him  to  adapt  the  other  to  it;  and  conse- 
quently that  which  is  active  in  certain  respects  is 
passive  from  another  point  of  view, — active  in  so  far 
as  that  which  we  distinctly  know  in  it  serves  to  give 
a   reason    for   that   which   occurs    in   another,    and 
passive  in  so  far  as  the  reason  for  what  transpires  in 
it    is   found    in  that  which   is  distinctly  known   in 
another. 

53.  Now  as  there  are  an  infinity  of  possible  uni- 
verses in  the  Ideas  of  God,  and  but  one  of  them  can 
exist,    there    must   be   a   sufficient    reason    for   the 


MONADOLOGY.  263 

choice  of  God  which  determines  him  to  select  one 
rather  than  another. 

54.  And  this  reason  is  to  be  found  only  in  the  fit- 
ness  or   in   the    degree  of   perfection   which    these 
worlds  possess,  each  possible  thing  having  the  right 
to  claim  existence  in  oroportion  to  the  perfection 
which  it  involves. 

55.  This    is  the  cause  for   the  existence  of   the 
greatest  good;     namely,   that    the  wisdom  of  God 
permits  him  to  know  it,  his  goodness  causes  him  to 
choose  it  and  his  power  enables  him  to  produce  it. 

56.  Now,    this    interconnection,    relationship,    or 
this  adaptation  of  all  things  to  each  particular  one, 
and  of  each  one  to  all  the  rest,  brings  it  about  that 
every  simple  substance  has  relations  which  express 
all  the  others  and  that  it  is  consequently  a  perpetual 
living  mirror  of  the  universe. 

57.  And  as  the  same  city  regarded  from  different 
sides  appears  entirely  different,  and  is,  as  it  were, 
multiplied  perspectively,  so,  because  of  the  infinite 
number  of   simple  substances,  there  are  a  similar 
infinite  number  of  universes  which  are,  nevertheless, 
only  the  aspects  of  a  single  one,  as  seen  from  the 
special  point  of  view  of  each  Monad. 

58.  Through    this  means  has  been  obtained  the 
greatest  possible  variety,  together  with  the  greatest 
order  that  may  be;  that  is  to  say,  through  this  means 
has  been  obtained  the  greatest  possible  perfection. 

59.  This  hypothesis,   moreover,  which  I  venture 
to  call  demonstrated,  is  the  only  one  which  fittingly 
gives  proper  prominence  to  the  greatness  of  God. 
Monsieur  Bayle  recognized    this  when  in  his  Dic- 
tionary (article  "Rorarius"),  he  raised  objections  to 
it;    indeed,  he  was  inclined  to  believe  that  I  attrib- 


264  LEIBNIZ. 

uted  too  much  to  God,  and  more  than  should  be 
attributed.  But  he  was  unable  to  bring  forward 
any  reason  why  this  universal  harmony,  which 
causes  every  substance  to  express  exactly  all  others, 
through  the  relation  which  it  has  with  them,  is 
impossible. 

60.  Besides,  in  what  has  just  been  said,   can  be 
seen    the   a  priori  reasons   why   things   cannot    be 
otherwise  than  they  are.      It    is   because  God,    in 
ordering  the  whole,  has  had  regard  to  every  part 
and  in  particular  to  each  Monad  whose  nature  it  is 
to  represent.      Therefore,    nothing  can  limit  it  to 
represent  merely  a  part  of  the  things.     It  is  never- 
theless true,  that  this  representation  is,  as  regards 
the  details  of  the  whole  universe,  only  a  confused 
representation,    and  is    distinct  only  as   regards  a 
small  part  of  them,  that  is  to  say,  as  regards  those 
things    which    are   nearest   or  most    in  relation   to 
each  Monad.     If  the  representation  were  distinct  as 
to  the  details  of  the  entire  universe,  each  Monad 
would  be  a  Deity.     It  is  not  in  the  object  repre- 
sented that  the  Monads  are  limited,  but  in  the  modi- 
fications of  their  knowledge  of  the  object.      In  a 
confused  way  they  reach  out  to  infinity  or  to  the 
whole,   but    are   limited   and  differentiated    in   the 
degree  of  their  distinct  perceptions. 

61.  In  this    respect  composites   are    like   simple 
substances.     For  all  space  is  filled  up;    therefore, 
all  matter  is  connected;    and  in  a  plenum  or  filled 
space  every  movement  has  an  effect  upon  bodies  in 
proportion  to  their  distance,    so  that    not   only  is 
every  body  affected  by  those  which  are  in  contact 
with    it,    and  responds    in  some   way  to   whatever 
happens  to  them,  but  also  by  means  of  them  the 


MONADOLOGV.  265 

body  responds  to  those  bodies  adjoining  them,  and 
their  intercommunication  can  be  continued  to  any 
distance  at  will.  Consequently  every  body  responds 
to  all  that  happens  in  the  universe,  so  that  he  who 
saw  all,  could  read  in  each  one  what  is  happening 
everywhere,  and  even  what  has  happened  and  what 
will  happen.  He  can  discover  in  the  present  what 
is  distant  both  as  regards  space  and  as  regards 
time;  O-U/U-TTVOIO.  iravra,  as  Hippocrates  said.  A  soul 
can,  however,  read  in  itself  only  what  is  there  rep- 
resented distinctly.  It  cannot  all  at  once  open  up 
all  its  folds,  because  they  extend  to  infinity. 

62.  Thus  although  each  created  Monad  represents 
the  whole  universe,  it  represents  more  distinctly  the 
body  which  specially  pertains  to  it,  and  of  which 
it   constitutes    the    entelechy.       And    as    the  body 
expresses  all  the  universe  through  the  interconnec- 
tion of  all  matter  in  the  plenum,  the  soul  also  rep- 
resents the  whole  universe  in  representing  this  body, 
which  belongs  to  it  in  a  particular  way. 

63.  The  body  belonging  to  a  Monad,  which  is  its 
entelechy  or    soul,    constitutes    together   with    the 
entelechy  what  may  be  called  a  living  being,   and 
with  a  soul  what    is  called  an  animal.     Now,  this 
body  of  a  living  being  or  of  an  animal  is  always 
organic,  because  every  Monad   is  a  mirror  of  the 
universe  according  to  its  own  fashion,  and,  since  the 
universe  is  regulated  with  perfect  order,  there  must 
needs  be  order  also  in  the  representative,  that  is  to 
say,  in  the  perceptions  of  the  soul  and  consequently 
in  the  body  through  which  the  universe  is  repre- 
sented in  the  soul. 

64.  Therefore,    every  organic    body  of   a   living 
being  is  a  kind  of  divine  machine,  or  natural  autom- 


266  LEIBNIZ. 

aton,  infinitely  surpassing  all  artificial  automatons. 
Because  a  machine  constructed  by  man's  skill  is 
not  a  machine  in  each  of  its  parts;  for  instance,  the 
teeth  of  a  brass  wheel  have  parts  or  bits  which  to  us 
are  not  artificial  products  and  contain  nothing  in 
themselves  to  show  the  use  to  which  the  wheel  was 
destined  in  the  machine.  The  machines  of  nature, 
however,  that  is  to  say,  living  bodies,  are  still 
machines  in  their  smallest  parts  ad  infinitum.  Such 
is  the  difference  between  nature  and  art,  that  is  to 
say,  between  Divine  art  and  ours. 

65.  The  author  of  nature  has  been  able  to  employ 
this  divine  and  infinitely  marvellous  artifice,  because 
each  portion  of  matter  is  not  only,  as  the  ancients 
recognized,  infinitely  divisible,  but  also  because  it 
is  really  divided  without  end,  every  part  into  other 
parts,  each  one  of  which  has  its  own  proper  motion. 
Otherwise  it  would  be  impossible  for  each  portion 
of  matter  to  express  all  the  universe. 

66.  Whence  we  see  that  there  is  a  world  of  created 
things,  of  living  beings,  of  animals,  of  entelechies, 
of  souls,  in  the  minutest  particle  of  matter. 

67.  Every  portion  of  matter  may  be  conceived  as 
like  a  garden  full  of  plants,  and  like  a  pond  full  of 
fish.     But  every  branch  of  a  plant,  every  member  of 
an  animal,  and  every  drop  of  the  fluids  within  it,  is 
also  such  a  garden  or  such  a  pond. 

68.  And  although  the  ground  and  the  air  which 
lies  between  the  plants  of  the  garden,  and  the  water 
which  is  between  the  fish  in  the  pond,  are  not  them- 
selves plant  or  fish,  yet  they  nevertheless  contain 
these,  usually  so  small,  however,  as  to  be  impercep- 
tible to  us. 

69.  There  is,  therefore,  nothing  uncultivated,   or 


MONADOLOGY.  267 

sterile  or  dead  in  the  universe,  no  chaos,  no  con- 
fusion, save  in  appearance;  somewhat  as  a  pond 
would  appear  at  a  distance  when  we  could  see  in  it 
a  confused  movement,  and  so  to  speak,  a  swarming 
of  the  fish,  without,  however,  discerning  the  fish 
themselves. 

70.  It  is  evident,  then,  that  every  living  body  has  a 
dominating  entelechy,  which  in  animals  is  the  soul. 
The  parts,  however,  of  this  living  body  are  full  of 
other  living  beings,   plants  and  animals,  which,  in 
turn,   have  each  one   its    entelechy  or   dominating 
soul. 

71.  This  does  not  mean,  as  some  who  have  mis- 
understood my  thought  have   imagined,  that  each 
soul  has  a  quantity  or  portion  of  matter  appropriated 
to  it  or  attached  to  itself  for  ever,  and  that  it  conse- 
quently owns  other  inferior  living  beings  destined 
to  serve  it  always;    because  all  bodies  are  in  a  state 
of  perpetual  flux  like  rivers,  and  the  parts  are  con- 
tinually entering  in  and  passing  out. 

72.  The  soul,   therefore,   changes   its   body  only 
gradually    and    by   degrees,    so    that    it    is    never 
deprived  all   at  once  of   all    its  organs.     There   is 
frequently  a  metamorphosis  in  animals,  but  never 
metempsychosis  or  a  transmigration  of  souls.  Neither 
are  there  souls  wholly  separate  from  bodies,  nor  bodi- 
less spirits.     God  alone  is  without  body. 

73.  This  is  also  why  there  is  never  absolute  gener- 
ation or  perfect  death  in  the  strict  sense,  consisting 
in  the  separation  of  the  soul  from  the  body.     That 
which    we    call    generation    is     development    and 
growth,  and  that  which  we  call  death  is  envelop- 
ment and  diminution. 

74.  Philosophers    have  been  much  perplexed   in 


268  LEIBNIZ, 

t 

accounting  for  the  origin  of  forms,  entelechies,  or 
souls.  To-day,  however,  when  it  has  been  learned 
through  careful  investigations  made  in  plant,  insect, 
and  animal  life,  that  the  organic  bodies  of  nature 
are  never  the  product  of  chaos  or  putrefaction,  but 
always  come  from  seeds  in  which  there  was  without 
doubt  some  preformation,  it  has  been  decided  that 
not  only  is  the  organic  body  already  present  before 
conception,  but  also  that  a  soul,  in  a  word,  the  ani- 
mal itself,  is  also  in  this  body;  and  it  has  been 
decided  that,  by  means  of  conception  the  animal  is 
disposed  for  a  great  transformation,  so  as  to  become 
an  animal  of  another  species.  We  can  see  cases 
somewhat  similar  outside  of  generation  when  grubs 
become  flies  and  caterpillars  become  butterflies. 

75.  These  little  animals,  some  of  which,  by  con- 
ception, become  large  animals,  may  be  called  sper- 
matic.    Those  among  them  which  remain  in  their 
species,  that  is  to  say,  the  greater  part,  are  born, 
multiply,  and  are  destroyed,  like  the  larger  animals. 
There  are  only  a  few  chosen  ones  which  come  out 
upon  a  greater  stage. 

76.  This,    however,    is   only  half    the    truth.      I 
believe,  therefore,  that  if  the  animal  never  actually 
commences  in  nature,  no  more  does  it  by  natural 
means  come  to  an  end.     Not  only  is  there  no  gener- 
ation, but  also  there  is  no  entire  destruction  or  abso- 
lute    death.       These     reasonings,     carried     on     a 
posteriori,     and     drawn     from     experience,     accord 
perfectly  with  the  principles  which  I  have  above 
deduced  a  priori. 

77.  Therefore,  we  may  say,  that  not  only  the  soul 
(the  mirror  of  an  indestructible  universe)   is  inde- 
structible, but  also  the  animal  itself  is,  although  its 


MONADOLOGY.  269 

mechanism     is    frequently  destroyed   in   parts  and 
although  it  puts  off  and  takes  on  organic  coatings. 

78.  These  principles  have  furnished  me  the  means 
of   explaining  on    natural  grounds    the   union,    or, 
rather   the   conformity  between    the   soul    and   the 
organic  body.     The  soul  follows  its  own  laws,  and 
the  body  has  its  laws.    They  are  fitted  to  each  other 
in  virtue  of  the  pre-established  harmony  between  all 
substances,  since  they  are  all  representations  of  one 
and  the  same  universe. 

79.  Souls  act  in  accordance  with  the  laws  of  final 
causes  through  their  desires,  purposes  and  means. 
Bodies  act  in  accordance  with  the  laws  of  efficient 
causes   or   of    motion.      The    two   realms,    that   of 
efficient  causes  and  that  of  final  causes,  are  in  har- 
mony, each  with  the  other. 

80.  Descartes  saw  that  souls  cannot  at  all  impart 
force  to  bodies,  because  there  is  always  the  same 
quantity  of  force  in  matter.     Yet,  he  thought  that 
the  soul  could  change  the  direction  of  bodies.     This 
was,    however,   because    at    that  .  time   the   law  of 
nature,  which  affirms  also  the  conservation  of  the 
same  total  direction  in  the  motion  of  matter,  was 
not  known.     If  he  had  known  that  law,  he  would 
have  fallen  upon  my  system  of  Pre-established  Har- 
mony. 

81.  According  to  this  system  bodies  act  as  if  (to 
suppose  the  impossible)   there  were  no  souls  at  all, 
and  souls  act  as  if  there  were  no  bodies,  and  yet  both 
body  and  soul  act  as  if  the  one  were  influencing  the 
other. 

82.  Although    I    find    that   essentially   the  same 
thing  is  true  of  all  living  things  and  animals,  which 
we  have  just  said,  namely,   that  animals  and  souls 


370  LEIBNIZ. 

begin  from  the  very  commencement  of  the  world 
and  that  they  come  to  an  end  no  more  than  does  the 
world,  there  is,  as  far  as  minds  or  rational  souls  are 
concerned  nevertheless,  this  thing  peculiar,  that  their 
little  spermatic  progenitors,  as  long  as  they  remain 
such,  have  only  ordinary  or  sensuous  souls,  but  those 
of  them  which  are,  so  to  speak,  elevated,  attain  by 
actual  conception  to  human  nature,  and  their  sen- 
suous souls  are  raised  to  the  rank  of  reason  and  to 
the  prerogative  of  minds. 

83.  Among  the  differences  that  there  are  between 
ordinary  souls   and   spirits,  some  of  which  I   have 
already  instanced,  there  is  also  this  that,  while  souls 
in  general  are  living  mirrors  or  images  of  the  uni- 
verse of  created  things,  minds  are  also  images  of  the 
Deity  himself  or  of  the  author  of  nature.      They 
are  capable  of  knowing  the  system  of  the  universe, 
and  to  imitate  it  somewhat  by  means  of  architec- 
tonic patterns,  each  mind  being  like  a  small  divinity 
in  its  sphere. 

84.  Therefore,  spirits  are  able  to  enter  into  a  sort 
of  social  relationship  with  God,  and  with  respect  to 
them   he  is  not  only  what  an   inventor    is   to  his 
machine   (as    is   his    relation  to  the  other  created 
things),  but  he  is  also  what  a  prince  is  to  his  sub- 
jects, and  even  what  a  father  is  to  his  children. 

85.  Whence    it    is    easy   to    conclude    that    the 
totality  of  all  the  spirits  must  compose  the  city  of 
God,  that  is  to  say,  the  most  perfect  state  that  is 
possible  under  the  most  perfect  monarch. 

86.  This  city  of  God,   this  truly  universal  mon- 
archy, is  a  moral  world  within  the  natural  world.     It 
is  what  is  noblest  and  most  divine  among  the  works 
of  God.     And  in  it  consists  in  reality  the  glory  of 


MONADOLOGY.  271 

God,  because  he  would  have  no  glory  were  not  his 
greatness  and  goodness  known  and  wondered  at  by 
spirits.  It  is  also  in  relation  to  this  divine  city  that 
God  properly  has  goodness.  His  wisdom  and  his 
power  are  shown  everywhere. 

87.  As  we  established  above  that  there  is  a  perfect 
harmony  between  the  two  natural  realms  of  efficient 
and  final  causes,  it  will  be  in  place  here  to  point  out 
another  harmony  which  appears  between  the  phys- 
ical realm  of  nature  and  the  moral  realm  of  grace, 
that    is   to   say,    between    God,    considered    as    the 
architect  of  the  mechanism  of  the  world  and  God 
considered   as  the   Monarch  of  the  divine  city  of 
spirits. 

88.  This    harmony   brings    it    about   that  things 
progress  of  themselves  toward  grace  along  natural 
lines,  and   that    this   earth,  for   example,  must   be 
destroyed  and  restored  by  natural  means  at  those 
times    when     the    proper    government    of     spirits 
demands  it,  for  chastisement  in  the  one  case  and 
for  a  reward  in  the  other. 

89.  We  can  say  also  that  God,  the  Architect,  satis- 
fies in  all  respects  God  the  Law-Giver,  that  there- 
fore sins  will  bring  their  own    penalty  with  them 
through  the  order  of  nature,  and  because  of  the  very 
mechanical  structure  of  things.     And  in  the  same 
way  the  good  actions  will  attain  their  rewards  in 
mechanical  ways  through  their  relation  to  bodies, 
although  this  cannot,  and  ought  not,  always  to  take 
place  without  delay. 

90.  Finally,  under  this  perfect  government,  there 
will    be   no    good  action   unrewarded    and    no   evil 
action  unpunished;    everything  should  turn  out  for 
the  well-being  of  the  good;    that  is  to  say,  of  those 


272  LEIBNIZ. 

who  are  not  disaffected  in  this  great  state,  who, 
after  having  done  their  duty,  trust  in  Providence 
and  who  love  and  imitate,  as  is  meet,  the  Author  of 
all  Good,  delighting  in  the  contemplation  of  his 
perfections  according  to  the  nature  of  that  genuine, 
pure  love  which  finds  pleasure  in  the  happiness  of 
those  who  are  loved.  It  is  for  this  reason  that  wise 
and  virtuous  persons  work  in  behalf  of  everything 
which  seems  conformable  to  the  presumptive  or 
antecedent  will,  and  are,  nevertheless,  content  with 
what  God  actually  brings  to  pass  through  his  secret, 
consequent  and  determining  will,  recognizing  that 
if  we  were  able  to  understand  sufficiently  well  the 
order  of  the  universe,  we  should  find  that  it  goes 
beyond  all  the  desires  of  the  wisest  of  us,  and  that 
it  is  impossible  to  have  it  better  than  it  is,  not  only 
for  all  in  general,  but  also  for  each  one  of  us  in  par- 
ticular, provided  that  we  cleave  as  we  should  to  the 
Author  of  all.  For  he  is  not  only  the  Architect  and 
the  efficient  cause  of  our  being,  but  he  is  also  our 
Lord  and  the  Final  Cause,  who  ought  to  be  the 
whole  goal  of  our  will,  and  who,  alone,  can  make 
our  happiness. 


INDEX. 


Abraham,  208,  230. 

Action  and  passion,  262. 

Activity  and  passivity,  13  et  seq. 

Acts,  reflective,  257. 

Adam,  concept  of,  73  et  seq.,  go  et 
seq.,  108  et  seq.,  120  et  seq.,  238. 

Aggregation,  197. 

Agreement.  See  Concomitance  and 
Freest  abliihed  Harmony, 

Albertus  Magnus,  159,  219. 

Alexander  the  Great,  13,  238. 

Analysis,  140. 

Animals,  souls  of,  224,  265  ;  transfor- 
mation of,  207  et  seq.,  268. 

Apperception,  253. 

Appetition,  254. 

Archimedes,  107,  170,  216. 

Aristotle,  xi,  45. 

Arnauld,  x,  et  seq.,  xix ;  letters  to 
Count  Ernst  von  Hessen-Rheinfels, 
72-74,100-103,209-210;  to  Leibnitz, 
88-100,  142-149,  172-180,  203-209 ; 
Leibnitz  to,  119-136,  136-142,  149- 
157,  157-168,  180-199,  201-203,  211- 
237,  239-242,  242-248. 

Atoms,  xiv  et  seq,,  221,  251  et  seq. 

Attributes,  252. 

Automatons,  255,  265. 

Averroes,  220. 

Axioms,  258. 

Bacon,  John,  219. 

Bayle,  254,  263. 

Beauty,  principles  of,  4  et  seq. 

Being,  a,  17,  191. 

Berkeley,  xv. 

Biel,  Gabriel,  219. 

Body,  xviii  et  seq.,  145  et  seq.,  244; 

and  soul,  relation  between  the,  56; 

153,  159.  171,  244- 
Boineburg,  viii. 


Bouillier,  v. 

Brunswick,  history  of,  139,  236,  242. 

Caesar,  Julius,  concept  of,  20  et  seq. 

Calculating  machine,  149. 

Calculus  of  increments,  248 

Calculus,  universal,  241. 

Canons,  practical,  258. 

Catelan,  Abbe,  168,  180,  199,  201,  209, 
235  et  seq.,  239  et  seq. 

Catholic  Church,  74,  200,  210. 

Causal,  definition  of,  41  et  seq. 

Causes,  model,  151 ;  efficient,  37,  173; 
occasional,  173, 182  et  seq.,  203,  214; 
final,  33  et  seq.,  272  ;  metaphysical 
136. 

Characteristic,  general,  241. 

Charity,  245. 

Charlemagne,  86. 

Christ,  Jesus,  62  et  seq.,  72. 

Cicati,  102,  103. 

City  of  God,  60. 

Clarke,  ix. 

Composites,  251  et  seq.,  264. 

Concept,  individual,  89,  95  et  seq., 
103  et  seq. 

Conceptions,  45  et  seq. 

Concomitance  or  the  agreement  of 
substances,  134,  149  et  seq.,  152  et 
seq.,  187.  See  Prelstablished  Har- 
mony. 

Consciousness,  253. 

Contingent  truths,  117. 

Continuum,  156,  162. 

Contradiction,  principle  of,  141. 

Contradictions,  258. 

Cordemoy,  163,  190,  205,  221. 

Corporeal  substance,  163. 

Correspondency,  laws  of,  215.  (See 
Preestablished  Harmony.} 

Created  thing,  261. 


274 


INDEX. 


Darius,  14. 

Death,  155. 

Definition,  42  et  seq.,  258. 

Democritus,  x,  xiii,  196. 

Descartes,  his  philosophy,  v  et  seq., 

29,  31,  139  et  seq.,  148,  152,  167  et 

seq.,  186,  202,  212,  219,  237,  240  et 

seq.,  261,  269. 
De  Sluse,  139. 
Diamonds  of  the   Grand  Duke  and 

the  Great  Mogul,  190. 
Du  Cange,  242. 
Duke  Ernst-Augustus,  ix. 
Duncan,  G.  M.,  ix. 
Durandus,  88. 
Duton,  ix. 

Efficient  causes,  37,  173. 
Ego,  xviii,  58,  179. 
Election,  52. 
Emperor  Henry  II.,  139. 
Entelechies,  253,  254,  266. 
Epicurus,  xi,  xiii,  190. 
Equations,  140. 
Erdmann,  ix. 

Essences,  particular,  their    expres- 
sion includes  everything,  27  et  seq. 
Essential,  definition  of,  41  et  seq. 
Este,  House  of,  242. 
Euclid,  141. 
Euler,  xvi,  xviii. 

Express,  the  word,  203,  211  et  seq. 
Extension,  x,  18,  155,  192. 

Fact,  258. 

Faith,  52. 

Fermat,  39. 

Fichte,  xv. 

Final  causes,  33  et  seq. 

Force,    God   always   preserves    the 

same  amount  of,  29  et  seq. 
Force,  measure  of,  29  et  seq.,  148  et 

seq.,  164  et  seq.,  246. 


Form,  192. 

,  15  et  seq.,  146 


,       . 

Forms,  substantial,  v,  15 
et  seq.,  174,  204. 

Galileo,  31,  170. 
Gassendi,  vii,  xiii. 
Geomancy,  10. 
Geometry,  36,  140. 


Gerhardt,  ix. 

God,  xv  et  seq.;  conception  of,  3  et 
seq.;  substances  like  a  mirror  of, 
15  ;  produces  different  correspond- 
ing substances,  23  et  seq.;  always 
preserves  the  same  amount  of 
force,  29  et  seq. ;  acts  upon  spirits, 
39;  only  immediate  object  of  our 
perceptions,  46  et  seq.;  action  of, 
upon  the  human  will,  48  et  seq.; 
grace  of,  51  et  seq.;  all  substances 
depend  upon,  54 ;  spirits  express, 
59;  city  of,  60,  270;  his  love,  62;  his 
freedom,  77  et  seq.;  his  knowledge, 
96;  resolutions  of,  inter-connection 
among  the,  104  et  seq.,  131 ;  free 
decrees  of,  122, 131 ;  his  perfection, 
234  ;  absolutely  perfect,  259  ;  the 
Necessary  Being,  260;  the  Final 
Cause,  272. 

Goodness,  principles  of,  4  et  seq. 

Grace  of  God,  51  et  seq. 

Grotefend,  ix. 

Guhrauer,  ix,  x. 

Harmonic  motion,  247. 

Heliodorus  of  Larissa,  39. 

Hermolaus  Barbarus,  261. 

Hessen-Rheinfels,  Leibnitz  to  Count 
Ernst  von,  67-72,  74-82,  82-88,  169- 
172,  199-201,  237-238;  Arnauld  to 
Count  Ernst  von,  72-74,  100-103,  209 
-210;  to  Leibnitz,  Count  Ernst  von, 
149,  210-211. 

Hippocrates,  265. 

Hudde,  139. 

Huygens,  199,  239  et  seq. 

Idea,  contemplation  of  the,  43  et  seq. 
Ideas,  we  think  by  means  of,  48. 
Immortality,  55,  57. 
Increments,  calculus  of,  248. 
Individual  concept,  19,  89,  95  et  seq., 

103  et  seq.,  149  et  seq. 
Individual  substance,  concept  of  our, 

49,  149,  163. 
Individual  substance  expresses  the 

whole  universe,  every,  133  et  seq. 
Isaac,  93,  230. 
Isochronous  curve,  239. 


INDEX. 


275 


Janet,  Paul,  ix. 
Jesuits,  87. 

Jesus  Christ,  62  et  seq.,  72. 
Jobert,  Father,  102. 
Judas,  48  et  seq. 
Jurieu,  209. 

Jurisprudence,  138,  242. 
Justel,  242. 
Justice,  245. 

Kant,  xvii. 

Kepler,  247. 

Knowledge,  170,  261 ;  clear  and  ob- 
-scure,  distinct  and  confused,  ade- 
quate and  inadequate,  intuitive  and 
assumed,  41  et  seq. 

Lagrange,  L.  P.,  v. 

Langley,  ix. 

I.atta,  ix. 

Leeuwenhoeck,  155,  227. 

Leibnitz,  his  philosophy,  Janet  on, 
v-xxi  ;  letters  to  Count  Ernst  von 
Hessen-Rheinfels,  67-72,  74-82,  82- 
88,  169-172,  199-201,  237-238;  Ar- 
nanld  to,  88-100,  142-149,  172-180, 
203-209 ;  his  remarks  upon  a  letter 
of  Arnauld,  103-119;  to  Arnauld, 
119-136,  136-142,  149-157,  157-168, 
180-199,  201-203,  211-237,  239-242, 
242-248  ;  Count  Ernst  von  Hessen- 
Rheinfels  to,  149,  210-211. 

Louys  de  Dole,  Father,  88. 

Luther,  101. 

Machine,  156,  177,  191  ;  divine,  265. 
Maim  burg,  86. 
Maine  de  Biran,  zxi. 
Malebranche,  vi,  xi,  83,  142,  201  et 

seq.,  241. 
Malpighi,  226. 
Mass,  29. 

Materialistic  philosophers,  36. 
Matter,  214  ;  extension  of,  32  et  seq.; 

phenomena  of,  32  et  seq. 
Me,  the  (See  Ego). 
Mechanicalism,  viii,  136. 
Mechanics,  141. 
Mciancthon,  loi. 
Melissus,  218. 
Memory,  57,  256. 


Metaphysical  causes,  136. 

Metaphysics,  summary  of  the  dis- 
course on,  68. 

Mind,  257. 

Miracles,  n,  184. 

Moliere,  vi. 

Monadology,  251-272. 

Monads,  x,  xii  et  seq.,  251  etseq. 

Morus,  219. 

Moses,  177. 

Motion,  xiv,  192;  quantity  of,  29  et 
seq.,  164  et  seq.;  laws  of,  167,  202, 
236;  perpetual,  167;  harmonic,  247; 
planetary,  laws  of,  247. 

Nainur,  Bishop  of,  10. 

Necessary  truths,  23,  170,  257. 

Nerves,  181. 

Newton,  xvi. 

Nicole,  vi,  209. 

Nominal,  definition  of,  41  et  seq. 

Occasional  causes,   153,   173,   182  et 

seq.,  203,  214. 
Order,  10  et  seq. 

Parmenides,  218,  223. 
Pascal,  148,  242. 
Passion,  action  and,  262. 
Passivity  and  activity,  13  et  seq. 
Perception,  253,  254. 
Perfection,  divine,  3  et  seq. 
Perpetual  motion,  166. 
Phcfdo,  35. 
Philoponus,  219. 
Philosophers,  materialistic,  36. 
Planetary  motion,  laws  of,  247. 
Plato,  35  et  seq.,  44  et  seq.,  70  et  seq., 

161,  218,  220,  223;  his  doctrine  of 

reminiscence,  44. 
Plenum,  264. 
Poiret,  261. 
Porus,  14. 
Postulates,  258. 
Power,  261. 

Predicate,  subject  and,  126. 
Predication,  13. 
Pre-established,  harmony,  xiii,  32  et 

seq.,  134  et  seq.,  143  et  seq.,  149  et 

seq.,  157  et  seq  ,  172  et  seq.,  185, 

187,  215,  263,  269  et  seq. 


276 


INDEX. 


Preformation,  268. 

Problems,  transcendental,  139  et  seq., 

248. 
Proclus,  219. 

Qualities,  occult,  vii. 
Quantity  of  directions,  187. 

Rational  soul,  257. 

Real,  definition  of,  41  et  seq. 

Reasoning,  258. 

Reason,  principle  of  sufficient,  258. 

Reflective  acts,  257. 

Refraction,  laws  of,  38. 

Regulations,  subordinate,  n. 

Reminiscence,  Plato's  doctrine  of, 44. 

RfSmond  de  Montmort,  ix. 

Republic  of  the  Universe,  245. 

Republic,  universal,  195. 

Roman  Catholic  Church,  200. 

Saint  Augustine,  51,  74,  89,  102,  144, 
153.  158,  175  et  seq.,  220. 

St.  Cunigunde,  139. 

St.  Gregory  the  Great,  86. 

St.  Paul,  53  et  seq. 

St.  Thomas,  14,  18,  in,  129,  155,  159, 
238. 

Samson,  93. 

>  aniuel,  93. 

Scholastic  philosophers,  17. 

Schulemburg,  ix. 

Sin,  51. 

Snellius,  38,  39. 

Socinians,  84  et  seq. 

Socrates,  35,  70. 

Soul,  xviii  et  seq.,  55,  145  et  seq.,  149, 
267 ;  union  of,  with  the  body,  56, 
153.  159.  171.  2441  rational,  257;  ani- 
mal, 265 ;  the  mirror  of  an  inde- 
structible universe,  268 ;  compared 
to  blank  tablets,  45  et  seq.;  indivis- 
ible and  indestructible,  155;  have 
brutes — ?  175  et  seq.;  great  number 
of,  194  ;  transmigration  of,  207  et 
seq. 

Speculative  theorems,  258. 

Sphere,  concept  of  the,  116. 

Spinoza,  xiii,  xvii,  241. 

Spirits,  270;  and  other  substances, 
difference  between,  57;  and  souls 


or  substantial  forms,  difference  be- 
tween, 57  ;  excellence  of,  59  ;  ex- 
press God,  59 ;  how  God  acts  upon, 
39- 

Spiritual  substance,  176. 

Subject  and  predicate,  126. 

Substance,  individual,  12  et  seq.,  49, 
112,  124,  162  ;  like  a  mirror  of  God, 
15  ;  action  of  one  upon  another,  26 
et  seq.;  corporeal,  163;  spiritual, 
176  ;  each  expresses  the  whole  uni- 
verse, 233  et  seq.,  263. 

Substances,  x  et  seq.,  244  ;  nature  of, 
23etseq.;  immaterial,  39;  possible, 
129  et  seq. ;  concomitance  and  agree- 
ment of,  134  et  seq.,  143  et  seq.,  157; 
simple,  251. 

Substantial  form,  174. 

Sufficient  reason,  principle  of,  258. 

Swammerdam,  228. 

Tangents,  248 ;  method  of,  139;  rule 

of,  240. 

Theologians,  17. 
Theorems,  speculative,  258. 
Things,  adaptation  of  all,  263. 
Thomists,  87. 
Thought,  169. 
Toletus,  vi. 
Transcendental  problems,  139  et  seq., 

248. 

Transcendentals,  240. 
Transformation,  160,  219,  228. 
Transmigration,  160,  219,  228. 
Truths,  necessary,  257,  260  et  seq; 

two  kinds  of,  258;  eternal,  260  et 

seq.;  contingent,  261. 

Unity,  substantial,  175,  189,  igi  et 

seq.,  204,  220  et  seq. 
Universe,  Republic  of  the,  245. 
Universes,  infinity  of  possible,  262. 

Vacuum,  xv  et  seq. 
Varillasi  86. 
Virtus  dorntitiva,  vi. 
Vortexes,  246. 

Will,  261 ;  action  of  God  upon  the 

human,  48  et  seq. 
Wisdom,  246. 


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218.  HYMNS  OF  THE  FAITH  (DHAMMAPADA),  being  an  Ancient 
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44-     WHENCE    AND    WHITHER.      The    Nature    of    the    Soul,    Its 
Origin  and  Destiny.     Paul  Carus.     250,  mailed  320.     (is.  6d.) 

45.  AN   ENQUIRY   CONCERNING  HUMAN   UNDERSTANDING. 

David  Hume.     3$c,  mailed  430.     (23.) 

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ALS.    David  Hume.     250,  mailed  310.     (is.  6d.) 


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Researches  in  Hypnotism.  Alfred  Bi.net.  Transl.  by  Adam 
Cowans  Whyte.  250,  mailed  310.  (is.  6d.) 

48.  A  TREATISE  CONCERNING  THE  PRINCIPLES  OF  HUMAN 

KNOWLEDGE.     George  Berkeley.     250,  mailed  310.    (is.  6d.) 

49-  THREE  DIALOGUES  BETWEEN  HYLAS  AND  PHILONOUS. 
George  Berkeley.  250,  mailed  300.  (is.  6d.) 

50.  PUBLIC  WORSHIP,  A  STUDY  IN  THE  PSYCHOLOGY  OF 

RELIGION.     John  P.  Hylan.     250,  mailed  290.     (is.  6d.) 

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CIPLES of  Rene  Descartes.  Transl.  by  Prof.  John  Veitch. 
35c,  mailed  420.  (25.) 

sa.  LEIBNIZ:  DISCOURSE  ON  METAPHYSICS,  CORRESPOND- 
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£oc,  mailed  $8c.  (23.  6d.) 

53.  KANT'S  PROLEGOMENA  to  any  Future  Metaphysics.  Edited 
by  Dr.  Paul  Carus.  soc,  mailed  sgc.  (23.  6d.) 

54  ST.  ANSELM:  PROSLOGIUM;  MONOLOGIUM;  AN  APPEN- 
DIX ON  BEHALF  OF  THE  FOOL,  by  Gaunilon;  and  CUR 
DEUS  HOMO.  Tr.  by  S.  N.  Deane.  soc,  mailed  6oc,  (23.  6d.) 

S3.  THE  CANON  OF  REASON  AND  VIRTUE  (LAO-TZE'S  TAO  TM 
KING).  Translated  from  the  Chinese  by  Paul  Carus.  250, 
mailed  280.  (is.  6d.) 

56.  ANTS    AND    SOME    OTHER    INSECTS,    an   Inquiry    into   the 

Psychic  Powers  of  these  Animals,  with  an  Appendix  on  the 
Peculiarities  of  Their  Olfactory  Sense.  Dr.  August  For  el. 
Transl.  by  Prof.  W.  M.  Wheeler,  soc,  mailed  530.  (23.  6d.) 

57.  THE  METAPHYSICAL   SYSTEM   OF  HOBBES,    as  contained 

in  twelve  chapters  from  his  "Elements  of  Philosophy  Concern- 
ing Body,"  and  in  briefer  Extracts  from  his  "Human  Nature" 
and  "Leviathan,"  selected  by  Mary  Whiton  Calkins.  400, 
mailed  470.  (23.) 

58.  LOCKE'S  ESSAYS  CONCERNING  HUMAN  UNDERSTAND- 

ING. Books  II  and  IV  (with  omissions).  Selected  by  Mary 
Whiton  Calkins,  soc,  mailed  6oc.  (23.  6d.) 

59.  THE   PRINCIPLES   OF   DESCARTES'   PHILOSOPHY.    Bene- 

dictus  de  Spinoza.  Introduction  by  Halbert  Mains  Britan,  Ph. 
D.  Paper,  350  net,  mailed  420. 

60.  THE  VOCATION  OF  MAN.     Johann  Gottlieb  Fichte.     Tr.  by 

William  Smith,  with  biographical  introduction  by  E.  Ritchie, 
1906.  250,  mailed  310.  (is.  6d.) 

61.  ARISTOTLE  ON  HIS  PREDECESSORS.     Being  the  first  book 

of  his  metaphysics.  Tr.  with  introduction  and  notes  by  A.  E. 
Taylor.  350,  postpaid.  (2.) 


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that  there  is  a  problem  to  be  solved;  there  must  be 
fault  somewhere  either  in  our  reasoning  or  in  our 
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